On April 8, Díaz’s first major league home run contributed to the Cardinals becoming the first team in major league history to hit three pinch hit home runs in the same game. Jeremy Hazelbaker and Greg Garcia were the other pinch hitters as the Cardinals defeated the Atlanta Braves, 7–4. The previous record of two pinch hit home runs by the same team in one game was previously accomplished on 57 occasions, most recently in 2011. Tejada was reinstated from the disabled list on April 18, However, Díaz’ hitting had led the Cardinals to instead retain him as the starting shortstop, thus assigning Tejada to be a utility infielder.

In his Cuban National Series career, Díaz totaled 342 games, batting .307, .397 OBP, .439 SLG, 193 runs scored, 54 doubles, 27 home runs and 165 runs batted in (RBI) in 1125 at bats. He defected from Cuba in 2012 while playing with the Cuban national baseball team in a tournament in the Netherlands. He was declared ineligible to sign with any MLB teams until February 19, 2014, due to lying about his age. He spent the interim 18 months from defecting from Cuba playing in Mexico City.

To audition for a contract with MLB clubs, Díaz held a showcase with fellow Cuban defector Odrisamer Despaigne on February 13, 2014. Although Díaz was initially projected to command a major league contract with a similar level of pay to other Cuban defectors such as Alex Guerrero and Erisbel Arruebarrena, his performance in the showcase did not leave the impression that he merited such a level of salary, and, further, many clubs passed on him altogether. He had left Mexico City effectively out of shape to play professional baseball. He signed a four-year contract with the St. Louis Cardinals worth $8 million on March 9.

The Cardinals first assigned Díaz to the Palm Beach Cardinals of the Class A-Advanced Florida State League in 2014, and he was promoted to the Springfield Cardinals of the Class AA Texas League that season. In 47 games between both teams, he batted .273/.324/.441 with five home runs, 24 RBIs, and seven stolen bases. In 2015, while playing for Springfield, he battled injuries before he was designated for assignment on July 8, 2015. While he had benefited from talent alone while playing in Cuba, his lack of preparation had caused his performance to suffer after playing the minor leagues. However, he diligently began to prepare more and proactively ask more questions.

Originally planning for Díaz to spend the 2016 season in Memphis, the Cardinals eventually moved three veteran players to accommodate him becoming the starting shortstop. On April 5, 2016, the Cardinals recalled him to the major league roster to take the place of outfielder Tommy Pham, who had departed on Opening Day two days earlier with an injury. Díaz debuted on the same day as his call-up. In his first major league at bat in the third inning against the Pittsburgh Pirates, he singled off Jon Niese for his first hit in a 6–5 loss. Initially, Díaz’ presence on the roster gave the Cardinals a capable hitter with upside who could play shortstop and fill a void until the return of Rubén Tejada, who had injured himself late in spring training. Tejada himself was a replacement signed as a free agent during spring training to replace the already-established starting shortstop Jhonny Peralta, who also had injured himself and was projected to be unable to play significantly longer than Tejada.

Díaz hit his first major league grand slam on September 27, 2016, his first game back after the death of his childhood friend, José Fernández. Díaz was called back out for a curtain call, where he rose his helmet high towards the sky. He stated afterwards, “Every time I put on a uniform, I will think of him.” Over his last 31 games of the season, he committed one error.

Díaz batted .300 in 111 games in his rookie year, with 121 hits, 28 doubles, 17 home runs, 69 RBIs, a .369 OBP, and a .510 SLG. He played 106 games at shortstop and was fourth in the league in errors with 16. In the 2016 NL Rookie of the Year voting, he placed fifth.

On April 8, 2017, Díaz hit two home runs for his first MLB multi-home run game, with one of those home runs sticking to the “G” letter of the Big Mac Land sign at Busch Stadium. The Cardinals won 10–4 over the Cincinnati Reds. Diaz began the season with a .217 batting average, and improved in the month of May. The Cardinals optioned him to Memphis on June 28, after batting .260/.293/.396, seven home runs and 20 RBIs in 71 games. He eventually lost his role as the Cardinals’ starting shortstop with the emergence of rookie Paul DeJong—who finished second in the NL Rookie of the Year balloting—as a powerful batter and capable fielder. In the final game of the 2017 season, Díaz tore his hamstring.

The Cardinals traded Díaz to the Toronto Blue Jays on December 1, 2017, for minor league outfielder J. B. Woodman. He began the season as Toronto’s starting shortstop as Troy Tulowitzki was on the disabled list. On May 8, Díaz was placed on the disabled list with a left ankle sprain. In 110 plate appearances prior to being placed on the disabled list, he was batting .216/.273/.431 with six home runs and 13 RBIs. He was activated on June 1. For the season, Díaz hit .263/.303/.453 with 18 home runs and 55 RBIs in 130 games.

On November 17, 2018, the Blue Jays traded Díaz to the Houston Astros in exchange for minor league pitcher Trent Thornton. In 2019, he batted .271/.356/.467 with nine home runs and 40 RBIs in 210 at bats.

In 2020 he batted .241/.254/.483 with three home runs and six RBIs in 58 at bats.