In his first season at Utah, Wright immediately became one of the top players in the Pac-12 Conference. He finished in the top 10 in the conference in scoring, assists, steals, blocked shots, field goal percentage and free throw percentage. Wright additionally averaged 6.8 rebounds per game, despite playing the guard position. At the conclusion of the 2013–14 season, Wright became the first Ute to be named first-team All-Pac-12 and was also named to the league's All-Defensive team. Following the season, Wright considered entering the 2014 NBA draft, but ultimately decided to return to Utah for his senior season. At the start of his senior season, Wright was named to the 50-man watch lists for the Naismith College Player of the Year and the John R. Wooden Award. For the second-straight season, he was voted first-team All-Pac-12 and again named to the Pac-12 All-Defensive Team. Wright was also a two-time member of the Pac-12 All-Defensive team and won the 2015 Bob Cousy Award. Wright became the first player in Utah men's basketball history to be named to the first-team All-Pac-12 in consecutive years.
On June 25, 2015, Wright was selected with the 20th overall pick in the 2015 NBA draft by the Toronto Raptors. On July 3, 2015, he signed his rookie scale contract with the Raptors and joined the team for the 2015 NBA Summer League. On April 8, 2016, with All-Stars DeMar DeRozan and Kyle Lowry rested, Wright scored a season-high 19 points in a 111–98 win over the Indiana Pacers. During his rookie season, he had multiple assignments with Raptors 905 of the NBA Development League. Wright missed much of the 2016–17 season with a right shoulder injury. He also had multiple assignments to Raptors 905. On January 3, 2018, Wright set career highs with 25 points and 13 rebounds in a 124–115 win over the Chicago Bulls. He had his first career double-double and hit four 3-pointers to lead the second unit.
On February 7, 2019, Wright, C. J. Miles, Jonas Valančiūnas and a 2024 second-round draft pick were traded to the Memphis Grizzlies in exchange for Marc Gasol. On April 5, he scored a career-high 26 points in a 122–112 victory over the Dallas Mavericks. He also recorded his first career triple-double adding 14 assists and 10 rebounds. Two days later, on April 7, Wright posted his second triple-double with 20 points, 12 assists and 13 rebounds in a 129–127 victory over the Dallas Mavericks. On April 10, Wright posted his third triple-double with 13 points, 11 rebounds and 11 assists in a 132–117 win over the Golden State Warriors.
Dallas Mavericks (2019–present)
On July 8, 2019, Wright was acquired by the Dallas Mavericks in a sign-and-trade deal with the Memphis Grizzlies in exchange for two-second-round picks and the draft rights to Satnam Singh.