Parrish reached the major leagues in 1977 on a part-time basis, and by 1979, he had replaced Milt May as the team’s regular catcher. In 1979, he also played winter baseball in Puerto Rico with the Mayagüez Indians. Parrish hit for a .286 batting average along with 24 home runs and 82 runs batted in during the 1980 season to earn his first American League All-Star team berth as well as winning his first Silver Slugger Award.

Parrish’s most productive offensive season was 1982 when he posted a .284 batting average with 32 home runs and 87 runs batted in, winning another Silver Slugger Award in the process. He followed that in 1983 with 27 home runs and 114 runs batted in, earning his third Silver Slugger Award and winning his first Gold Glove Award. Parrish was an integral member of the world championship-winning 1984 Detroit Tigers team. Batting as the clean-up hitter, he produced 33 home runs and 98 runs batted in, adding another Silver Slugger Award as well as a second Gold Glove Award to his credentials. He also caught Jack Morris’ no-hitter on April 7 of that season. The Tigers led the American League Eastern Division season from start to finish and defeated the Kansas City Royals in the 1984 American League Championship Series before winning the 1984 World Series against the San Diego Padres.

After ten years with the Tigers, Parrish signed with the Philadelphia Phillies as a free agent before the 1987 season. The Phillies’ season slogan was “Lance us a Pennant.” He quickly fell out of favor with the Philadelphia fans and media in his second season there as a result of poor offensive output, ranking near the bottom of full-time Major League players in 1988 with a .215 batting average. Afterward, he played three seasons and parts of a fourth with the California Angels before ending his career with short stints for the Mariners, Indians, Pirates, and Blue Jays. Parrish was also with the Los Angeles Dodgers in spring training 1993, but he failed to make the squad because rookie Mike Piazza’s performance showed the club that Piazza was ready to be a starting Major League catcher. Parrish also signed to return to the Tigers in 1994, but his contract was purchased by the Pirates before he ever got back to the majors with Detroit. He signed with the Royals in 1995 but was traded to Toronto before he appeared in any Major League games with Kansas City. He signed once again with Pittsburgh in 1996 but did not make the team.

In a 19-year Major League career, Parrish played in 1,988 games, accumulating 1,782 hits in 7,067 at bats for a .252 career batting average along with 324 home runs and 1,070 runs batted in. Parrish was an eight-time All-Star (1980, 1982–86, 1988, and 1990), and he won three Gold Glove Awards (1983–85). Parrish was a six-time winner of the Silver Slugger Award, which is awarded annually to the best offensive player at each position. In 1982, he established the American League record for home runs by a catcher (32), surpassing the previous mark set by Yogi Berra and Gus Triandos; he beat his own mark two years later, with 33. Parrish ranks sixth in Major League history in home runs as a catcher with 299, making him 10th among catchers in total bases with 3,113 total bags and 11th in runs batted in with 1,070. He led American League catchers twice in baserunners caught stealing, once in assists, and once in caught stealing percentage. Parrish finished second in fielding percentage four times and ended his career with a .991 fielding percentage.

He became a Minor League manager with the Ogden Raptors, the Dodgers’ rookie-level team, for the 2006 season. The team finished 37-39. On November 20, 2006, he was hired to manage the Great Lakes Loons in Single-A ball during their debut season. His contract was not renewed following the season.

On February 5, 2014, Parrish was named manager of the Double-A affiliate of the Detroit Tigers, the Erie SeaWolves. He most recently served as the manager of Single-A West Michigan Whitecaps of the Midwest League. On November 12, 2019, Parrish was named special assistant to the general manager for the Tigers.