Rodriguez was born in 1947 in Cananea, Sonora, Mexico. He was part of a family with four sons and two daughters. His father, Aurelio Rodriguez Sr. played baseball in the Mexican League and was a member of the Mexican team that played in the 1953 world amateur tournament. Rodriguez learned to play baseball from his father, who told him that if he could field on the stone-covered diamonds of Cananea, he could field anywhere.

Rodriguez began playing professional baseball in Mexico at age 16. In 1965, he played in the Mexican League junior league for the Mineros de Fresnero and at the end of the season was promoted to the Charros de Jalisco. In 1966, he played 135 games at shortstop for Jalisco and compiled a .302 batting average with 15 triples and 54 RBIs. He was selected as the Mexican League’s 1966 Rookie of the Year.

In August 1966, Rodríguez signed with the California Angels. He was assigned to the Seattle Angels of the Pacific Coast League, playing at shortstop and compiling a .254 batting average in 59 at bats during the 1966 season. He moved to third base in 1967, playing most of the season for Seattle and El Paso. He hit .308 for Seattle and .327 at El Paso and had 32 doubles, nine triples, 13 home runs and 64 RBIs in 315 at bats in the minors during the 1967 season.

Rodriguez made his major league debut at the age of 19 with the Angels in September 1967. From 1967 to 1971, he appeared in 281 games for the Angels, 264 as the team’s starting third baseman. While his .237 batting average was disappointing, he emerged as one of the American League’s best defensive third basemen. In May 1968, Angels coach Don Heffner described Rodriguez as “the kind of player who can play anyplace” and predicted that Aurelio would be “around for a long time.” Angels manager Bill Rigney boasted in March 1969: “He might be another Bobby Avila. Aurelio Rodriguez could be the best Mexican player ever.”

In 1969, Rodriguez appeared in 159 games at third base and led the league’s third basemen with 42 double plays turned and ranked second behind Brooks Robinson with 352 assists. On the other hand, his batting average was only .232, and he also led the league with 24 errors at third base in 1969. The most memorable error involving Rodriguez in 1969 was his Topps baseball card; the photograph on the card was actually the Angels’ batboy, Leonard Garcia.

Rodriguez developed a reputation as a ladies’ man. When asked in 1969 if he preferred American or Mexican girls, he smiled and replied that “as long as they wear skirts he likes them all.” A woman wrote in 1973 that Rodriguez had a “charm that attracts large numbers of woman fans. His handsome looks and disposition make the girls swoon.”

Rodriguez fell from favor in 1970 under the team’s new manager, Lefty Phillips. In March 1970, Phillips said: “We have tried everything to get Aurelio to choke up on the bat and to spray the ball instead of trying to pull for power but he won’t listen or try to correct himself. He just smiles at you, says ‘Si, amigo’ and then goes back to his old swing. It’s very frustrating.”

On April 26, 1970, the Angels traded Rodriguez with Rick Reichardt to the Washington Senators in exchange for power-hitting third baseman Ken McMullen. Washington manager Ted Williams said at the time that he hand-picked Reichardt and Rodriguez as players he would like to work with. Rodriguez appeared in 142 games for the Senators in 1970, including 137 games as the team’s starting third baseman. Under Williams’ tutelage in 1970, Rodriguez’s batting average increased modestly to .247, and he posted career highs with 19 home runs, 83 RBIs, 70 runs scored, and 15 stolen bases. Rodriguez later touted the lessons he learned from Williams: “He help me a lot. When I play for California I swing at too many bad balls. Not with Washington. Ted Williams, all the time, he say to me ‘no swing at bad balls … always look, look … wait … wait … I no forget what he tell me. Never.”

Rodriguez’s 19 home runs in 1970 was the most ever by a Mexican player in the major leagues — surpassing Bobby Avila’s mark of 15 home runs in 1954. On breaking Avila’s record, Rodriguez noted that Avila had been “a big hero” for Rodriguez while growing up.

During the 1970 season, Rodriguez also established himself as having a solid claim to being the most dominant defensive third baseman in the game. He appeared in 153 combined games at the position (both for the Angels and Senators) and led all major league third basemen in both assists (377) and double plays turned (41). He also reduced his error count to 18 and ranked fourth among all basemen with a .965 fielding percentage — two one-hundredths behind major league leader Graig Nettles. His 30 total zone runs (a defensive metric utilizing play-by-play data) ranked as the highest in the major leagues at any position — eight zone runs higher than Nettles. Despite Rodriguez’s impressive defensive showing, Brooks Robinson maintained a lock on the Gold Glove Award — receiving the award for 16 consecutive seasons from 1960 to 1975.

On October 9, 1970, Rodriguez was part of a blockbuster trade that sent four Washington players (Rodriguez, Ed Brinkman, Joe Coleman, and Jim Hannan) to the Detroit Tigers in exchange for Denny McLain and three other players. Rodriguez was considered “the prize of the deal”, a third baseman with “quick reflexes, a fast glove and superb throwing arm.”

At Detroit’s 1971 spring training, Rodriguez quickly earned a reputation for his smiling and happy disposition. Detroit public relations director Hal Middlesworth called him “the most pleasant guy I’ve ever seen. Always smiling and always laughing.” The team’s doctor in 1975 declared Rodriguez one of the most perfectly adjusted people he had ever met, adding, “He is a completely happy person.”

Rodriguez was married in December 1971. He and his wife had a son, Aurelio, in approximately 1974.

In 1973, Rodriguez continued to struggle at the plate, as his batting average fell to .222 with nine home runs. He did, however, lead the Tigers with 27 doubles and 58 RBIs. On defense, he led the league with 160 games at the third base and a .971 fielding percentage (technically .00002 behind with Don Money) and ranked among the league’s premier players at the position with 135 putouts (second), 30 double plays turned (fourth), and 335 assists (fifth).

Rodriguez began the 1975 season saying he was no longer listening to people telling him to spray the ball to right field. He recalled the advice of his old manager: “Ted Williams did not tell me to hit the ball to right or to center or to left. He just said hit it hard and not worry about it.” Rodriguez’s more relaxed approach led to a modest improvement in his batting average to .245, and he led the team with 20 doubles and six triples. On June 19, 1975, Rodriguez hit his first career grand slam against the Kansas City Royals.

In 1976, Rodriguez appeared in the Tigers’ first 128 games, but missed the remainder of the season after sustaining an ankle injury sliding into second base on August 29. In the 128 games he played, Rodriguez hit .240 with eight home runs and 50 RBIs. He led all major league third basemen with a .978 fielding percentage (nine errors in 409 chances) and received his first and only Gold Glove Award award — the first American League third baseman since 1959 to beat out Brooks Robinson. He also ranked second behind Graig Nettles in range factor per nine innings at third base.

Injuries continued to slow Rodriguez in 1977. He injured the same ankle sliding into home plate on April 26 and missed five weeks. Even after returning from the injury, Rodriguez shared the third base position with Phil Mankowski — Rodgriguez started 83 games and Mankowski 78. Rodriguez was unhappy with his new part-time role: “I’m not used to sitting on the bench, watching all nine innings. I finally got the Golden Glove last year, and now I’m not playing. I feel bad about it” Rodriguez was then slowed further when he slipped in a bathtub on July 2 and sustained a hairline rib fracture below his right arm.

In 1978, Rodriguez appeared in 131 games at third base, but only 86 as the starter, as he continued to share the third base position with Phil Mankowski. Despite the limited playing time, Rodriguez had the highest full-season batting average of his major league career at .265. He also led the major leagues with a .987 fielding percentage at third base, making only four errors during the entire season.

Rodriguez played his final season for the Tigers in 1979. He appeared in 106 games, 97 as the team’s starting third baseman, and hit .254 with five home runs and 36 RBIs. He no longer ranked among the league’s leading third basemen in any defensive category.

Rodriguez appeared in 89 games for the Padres in 1980, 57 as the team’s starting third baseman. His batting average dropped precipitously to .200 in his first season in the National League.

On August 4, 1980, with Graig Nettles out with hepatitis, the New York Yankees purchased Rodriguez from the Padres. Rodriguez appeared in 52 games for the 1980 Yankees, 43 as the starting third baseman. In 1981, Rodriguez remained with the Yankees as a backup to Nettles and started only 11 games. He compiled a .346 batting average in 52 at bats. In the 1981 World Series, he became a starter after Graig Nettles was injured in Game 2 and hit .417 (5-for-12).

Rodriguez was traded twice in the off-season between the 1981 and 1982 seasons. He was first traded by the Yankees in November to the Toronto Blue Jays for a player to be named later. He was then traded by Toronto in early April to the Chicago White Sox in exchange for outfielder Wayne Nordhagen. While initially expecting to be a backup in Chicago, the Sox traded Jim Morrison to Oakland in mid-June, and Rodriguez became the team’s regular third baseman. Rodriguez appeared in 118 games for the White Sox in 1982, including 87 starts at third base. While batting only .241, Rodriguez put in a solid year defensively, finishing third among the league’s third basemen with a .969 fielding percentage and a 3.38 range factor per nine innings at third base.

In February 1983, Rodriguez signed with the Baltimore Orioles as a free agent. He appeared in 45 games for the Orioles but only 18 as the starting third baseman. His batting average dropped precipitously to .119 in 67 at bats with Baltimore. He was released by Orioles in August.

Three weeks after being released by Baltimore, Rodriguez signed for a second run with the White Sox. He started only six games for Chicago in 1983 and compiled a .200 batting average in 20 at bats. He played in his final major league game on October 1, 1983 at age 35.

After his playing career ended, Rodriguez worked as a manager, primarily in the Mexican League, from 1987 to 1997. He began by managing the Los Mochis club in 1987. He returned to the United States in 1989 as assistant coach for the Colorado Springs Sky Sox, a Triple-A farm team for the Cleveland Indians. In 1990, he worked for the Toledo Mud Hens. In 1991, he was the manager of the Sultanes de Monterrey and led the club to Mexican League championship. He then managed the Saltillo team in 1992 and the Industriales de Monterrey in 1993 and 1994. In 1995, he was the manager of the Broncos de Reynosa of the Mexican League. He led Reynosa to the North Zone title in 1995. He was suspended for the remainder of the 1996 seasons following an altercation in which he allegedly struck or bumped an umpire in May 1996. Rodriguez returned as manager at Reynosa in 1997, but he was replaced after the 1997 season.

In September 2000, Rodriguez was killed on a Saturday afternoon while visiting Detroit. As he left the El Rancho restaurant, he was struck by a vehicle that jumped the curb at the corner of Cavalry and West Vernor. Rodriguez was thrown into the air and then pinned under another car. He was extricated and transported to Henry Ford Hospital where he was pronounced dead.

In 17 major league seasons, Rodríguez was a .237 hitter with 124 home runs and 648 RBIs in 2,017 games. It was on defense that he left his mark. His career range factor of 3.215 per nine innings at third base ranks second in major league history, trailing only Darrell Evans. And his career tally 4,150 assists at third base ranked fifth in major league history at the time of his retirement.