In October 2010, Purvis reclassified from the high school class of 2013 to the class of 2012. He said his classes would be in order and he could not wait to go to college. In the spring of 2011, he committed to Louisville, but reopened his recruitment in May after Louisville assistant Tim Fuller went to Missouri. On September 30, 2011, he announced his intent to play for Mark Gottfried at N.C. State, choosing the Wolfpack over offers from Connecticut, Memphis, Duke, Missouri and Ohio State. He was the 2012 North Carolina Gatorade Player of the Year. Purvis played in the 2012 McDonald's All-American Boys Game. On April 14, 2012, Purvis compiled 22 points, two rebounds and three steals in the Jordan Brand Classic. He was named the co-MVP with Shabazz Muhammad. ESPN analyst DJ Quinn wrote, "In a short period of time, Purvis distinguished himself as an athletic, strong, scoring threat. Excellent off the drive and finishing in the paint, he's difficult to guard. There's an attacking presence he brings to the table, making him one of the best young offensive players in his age group." He drew some comparison to fellow Raleigh native John Wall, although Purvis tried to shrug off these comparison. According to ESPN, he was the 15th best recruit in his class. He was the 12th ranked recruit in his class according to Rivals.com.
College career
In his only year at N.C. State, Purvis played in 35 games and averaged 8.3 points and 2.4 rebounds per game. He shot 44 percent from the floor and 38.2 percent from the three-point line. He was named ACC Rookie of the Week on November 12. Purvis scored a season-high 21 against Boston College on February 27. However, his minutes fell off when coach Gottfried moved forward T.J. Warren into the starting lineup, and Purvis scored a total of 12 points and played an average of 12.8 minutes in the final four games. He announced he was transferring to Connecticut on April 5, 2013. He said that N.C. State was not a good fit and he wanted to go off on his own. In his redshirt season, he trained with Shabazz Napier. Purvis underwent shoulder surgery in December 2013. Purvis was forced to sit out a game in his sophomore season for playing in two summer leagues. Purvis was named AACplayer of the week on March 2, 2015, after registering 28 points, three assists and three steals in an 81-73 win against SMU. He was selected to the All-AAC Tournament Team after scoring 29 points against SMU in the championship game. He finished second on the team in points per game and 3-pointers and collected 2.4 rebounds per game. Purvis had 28 points in a win against UMass Lowell on December 20, 2015. As a junior, Purvis led the team in scoring with 12.8 points per game, to go with 72 assists and 32 steals in 36 games total. He led the Huskies to the NCAA Tournament, where they beat Colorado, then lost to Kansas in the second round. He declared for the 2016 NBA Draft, but declined to hire an agent and opted to return to Connecticut for his final season on May 5. Purvis worked out at Chris Paul's camp for guards in the summer.
After going undrafted in the 2017 NBA draft, Purvis joined the Utah Jazz for the 2017 NBA Summer League. On October 9, 2017, Purvis signed a non-guaranteed contract with the Orlando Magic, but was later waived by the Magic before the start of the season. On October 23, 2017, Purvis was included in training camp roster of the Lakeland Magic.
Orlando Magic (2018)
On March 8, 2018, the Orlando Magic had announced that they had signed Purvis to a 10-day contract. Purvis had his NBA debut one day later, playing in 10 minutes of action in a 94–88 loss to the Sacramento Kings. Purvis signed a second 10-day contract on March 18, and signed for the remainder of the season on March 28. On July 20, 2018, Purvis was traded to the Oklahoma City Thunder in exchange for Dakari Johnson and cash considerations. On July 23, 2018, Purvis was traded to the Boston Celtics in exchange for Abdel Nader. Oklahoma City also received cash considerations in the deal. On July 30, 2018, Purvis was waived by the Celtics.
Purvis signed with the Miami Heat on October 11, 2018. He was waived on October 13. Purvis was subsequently added to the roster of the Sioux Falls Skyforce. In 49 games played for the Skyforce, he averaged 14.5 points, 3.8 rebounds and 3.6 assists per game.
On July 27, 2019, Purvis signed a one-year deal with Hapoel Tel Aviv of the Israeli Premier League. On September 29, 2019, he parted ways with Hapoel after appearing in one pre-season tournament game.
Pallacanestro Cantù (2020–present)
On February 25, 2020, he has signed with Pallacanestro Cantù of the Italian LBA.
Career statistics
NBA
Regular season
College
National team career
On February 8, 2018, Purvis was selected to participate in USA World Cup Qualifying Team training camp.
Personal life
His godfather is N.C. Central coach LeVelle Moton. His mother is Shanda McNair. Although he is an only child, Purvis's mother adopted Tyrek Coger when he was in eighth grade. Coger died after a workout at Oklahoma State University on July 21, 2016.