Powell attended IMG Academy in Bradenton, Florida. As a senior, he averaged 23.2 points, 11.6 rebounds, 4.4 assists and 2.3 blocks per game.
Considered a five-star recruit by Rivals.com, Powell was listed as the No. 8 power forward and the No. 25 player in the nation in 2010.
As a freshman at Stanford in 2010–11, Powell earned Pac-10 All-Freshman Team honors. In 31 games (26 starts), he averaged 8.1 points and 5.2 rebounds per game.
As a sophomore in 2011–12, the Cardinal won the NIT championship, and Powell earned Pac-12 All-Academic Honorable Mention selection. In 35 games (11 starts), he averaged 5.8 points and 4.6 rebounds per game.
As a junior in 2012–13, Powell earned second-team NABC All-District, first-team All-Pac-12 and Pac-12 All-Academic second team honors. He was also named the Pac-12 Most Improved Player of the Year. In 34 games (all starts), he averaged 14.9 points to go with 8.4 rebounds per game.
As a senior in 2013–14, Powell earned first-team All-Pac-12 honors for the second straight year, and was named to the NCAA All-South Regional Team. He was also named the Pac-12 Scholar-Athlete of the Year and a Pac-12 All-Academic Honorable Mention selection. In 36 games (all starts), he averaged 14.0 points and 6.9 rebounds per game.
On June 26, 2014, Powell was selected with the 45th overall pick in the 2014 NBA draft by the Charlotte Hornets. On July 12, Powell's rights were traded, along with Brendan Haywood, to the Cleveland Cavaliers in exchange for Scotty Hopson and cash considerations. He then joined the Cavaliers for the NBA Summer League and signed with them on August 23. On September 25, he was traded, along with John Lucas III, Erik Murphy, Malcolm Thomas and the Cavaliers' 2016 and 2017 second-round picks, to the Boston Celtics in exchange for Keith Bogans and two future second-round picks. During his time with the Celtics, he was assigned multiple times to the Maine Red Claws of the NBA Development League.
On December 18, 2014, Powell was traded, along with Rajon Rondo, to the Dallas Mavericks in exchange for Jae Crowder, Jameer Nelson, Brandan Wright, a 2015 first-round pick and a 2016 second-round pick. On January 14, 2015, he scored a season-high 11 points on 5-for-7 shooting in a loss to the Denver Nuggets. He was assigned multiple times to the Texas Legends during his rookie season.
In July 2015, Powell joined the Mavericks for the 2015 NBA Summer League. On November 3, 2015, he recorded his first career double-double with 10 points and 10 rebounds in a loss to the Toronto Raptors. Four days later, he recorded a then career-high 15 points and 7 rebounds in a 107–98 win over the New Orleans Pelicans. He tied his career high of 15 points on January 17, 2016 in a loss to the San Antonio Spurs. On March 28, 2016, Powell made his first NBA start and scored a career-high 16 points in a 97–88 win over the Denver Nuggets.
On July 8, 2016, Powell re-signed with the Mavericks. On December 3, 2016, he set a new career high with 17 points in a 107–82 win over the Chicago Bulls.