Boynton made 7 of 11 shots from the field, including 6 of 9 from 3-point range.
Florida shot 53.5 from the field, including 11-of-21 from 3-point range.
The Gators (22-6, 10-3 Southeastern Conference) needed it, too. They had 15 turnovers in the first 27 minutes, an error-filled start that had coach Billy Donovan seething and the Tigers (14-13, 4-9) leading.
Florida eventually settled down and used a 26-4 run to turn a one-point deficit into a double-digit lead. Bradley Beal and Erving Walker were huge in the spurt. They finished with 13 points apiece. Walker added seven rebounds and five assists.
Boynton and Beal capped the big run with consecutive 3s that sent many of the home fans home.
Florida's biggest concern after that was the health of forward Will Yeguete, who injured his left ankle with a little more than 10 minutes to play.
Adrian Forbes led Auburn with 11 points. He was the team's only player in double figures. Kenny Gabriel fell hard to the court twice, and Chris Denson was helped to the locker room with an apparent knee injury.
Denson injured his right knee on a driving layup just before halftime. His basket put the Tigers ahead 30-27 and surely gave Donovan more ammunition to rip his players during the break.
Florida, coming off its best game of the season, a 30-point win at Arkansas, responded. But it didn't happen until after Auburn led 37-36 with 13:40 remaining. Beal and Boynton started the turnaround with back-to-back 3s.
Beal added a driving layup and a putback. Walker went coast to coast and got through three defenders for a basket. Even seldom-used guard Scottie Wilbekin got in on the scoring, with a 3. Auburn had no answers.
The Tigers shot 33.3 percent from the floor and made 6 of 17 from behind the arc. But losing Denson and Gabriel was tough to overcome.