[3] In the 2013–14 season, Napier was unanimously selected for the All-AAC first team, and was named the inaugural American Athletic Conference Player of the Year.

As a senior, Napier led Lawrence Academy to an undefeated season going 29–0 in 2010, as they won the New England Prep Class C title after defeating St. Mark's finishing with 23 points, 8 steals, and 8 assists as he was named Tournament MVP.

At the end of the regular season, Napier was named to the Big East All-Rookie team along with teammate Jeremy Lamb.

[13] Moving into the starting lineup as a sophomore for Connecticut, Napier was a preseason honorable mention All-Big East pick and a Bob Cousy Award candidate.

Napier notched his first career triple-double (the ninth in Connecticut men's basketball history) as he tallied 22 points, 12 rebounds and 13 assists against Coppin State on November 20, 2011.

[16] Connecticut earned a 9 seed in the NCAA Tournament, but fell short to Iowa State as the Huskies finished the season going 20–14 (8–10 in conference play).

On April 26, 2013, Napier opted to return to the team for his senior year along with teammates Ryan Boatright and DeAndre Daniels.

In the AAC Tournament, Napier was named to the All-Tournament team after leading the Huskies to the championship game before falling to Louisville.

In the NCAA Tournament, Connecticut earned a 7 seed as Napier led them under second year coach Kevin Ollie past St. Joseph's, Villanova, Iowa State, and won the East Regional final defeating Michigan State as Napier was named the East Regional Most Outstanding Player.

Connecticut finished the season 32–8 overall (12–6 in conference play), and Napier averaged 18.0 points, 5.9 rebounds, 4.9 assists, and 1.8 steals per game.

Napier, along with UConn teammates Niels Giffey and Tyler Olander, are the only Division I men's players in history to have won national championships as both freshmen and seniors.

[31] On April 1, 2015, Napier was ruled out for the rest of the season after undergoing successful surgery to repair a sports hernia.

[32] He recovered in time to join the Heat's summer league team in July to compete in Orlando and Las Vegas.

[33] On July 27, 2015, Napier was traded to the Orlando Magic, along with cash considerations, in exchange for a conditional 2016 second-round draft pick.

[37] On December 28, 2017, Napier, who started for the injured Damian Lillard, scored 15 of his season-high 23 points in the fourth quarter to help the Trail Blazers rally for a 114–110 victory over the Philadelphia 76ers.

[39] On December 29, he tied his career high with 32 points on 9-of-15 shooting from the field and 10 of 12 from the foul line in a 129–115 loss to the Milwaukee Bucks.

[43] On July 7, 2019, Napier, Treveon Graham, and D'Angelo Russell were sent to the Golden State Warriors as part of a trade package for Kevin Durant.

[44] The following day, Napier and Graham were traded to the Minnesota Timberwolves in exchange for the draft rights to Lior Eliyahu.

In December 2013, the then Puerto Rico men's national basketball team coach Paco Olmos held a meeting with Napier and Velásquez, where his program was explained.