TJ Warren scored a game-high 35 points and gave the Suns a 112-110 lead with a layup with 20.8 seconds to play.
Prince got to the left wing on the Hawks' ensuing possession and hit a tough, lean-in 3-pointer for the win. It was Prince's sixth 3-pointer of the day, a career-high.
Devin Booker scored 20 points for the Suns, but missed a contested baseline jumper as time expired.
Dennis Schroder added 21 points, six rebounds and six assists for the Hawks.
Booker gave Phoenix an 87-86 lead with a layup off a full-court pass from Shaquille Harrison as time expired on the third quarter.
Booker was coming off four straight games with 30 or more points but deferred to Warren in the early going against the Hawks. Booker had only four points in the first half. Warren had 21 points, 17 in the second quarter, helping the Suns battle back from a first-quarter deficit and tie the score at 56 at halftime.
Both teams are playing out the final six weeks of the regular season with their eyes on the future. The Suns, with Booker, Warren and Josh Jackson, appear to be several steps ahead of the Hawks in the rebuilding process. Atlanta, however, does have up to three first-round draft picks this summer.
The Hawks led 108-107 with 2:14 to play when the two teams got into a kerfuffle that resulted in the ejections of Atlanta guard Isaiah Taylor and Phoenix guard Elfrid Payton, and technical fouls on Prince and Jackson.
Phoenix continues its four-game road trip at Miami on Monday. The Suns will play at Oklahoma City and Charlotte before returning home March 12 to take on Cleveland.
The Hawks take off for a difficult two-game road swing, beginning with a trip to Toronto on Tuesday to take on the Raptors, who own the best record in the Eastern Conference.
--Field Level Media
Phoenix | Atlanta | |
TJ Warren 35 | Scoring | Taurean Prince 22 |
Elfrid Payton 14 | Assists | Dennis Schroder 6 |
Elfrid Payton 10 | Rebounds | Miles Plumlee 11 |
Marquese Chriss 3 | Free Throws Made | John Collins 2 |
Tyson Chandler 2 | Steals | John Collins 2 |
Marquese Chriss 4 | Blocks | Dewayne Dedmon 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Phoenix | 112 | 50.0 | 11-26 | 9-15 | 33 | 41 | 6 | 6 | 14 |
Atlanta | 113 | 45.7 | 17-33 | 10-12 | 23 | 49 | 5 | 7 | 16 |