The Huskies (7-5) overcame a 13-point deficit in the second half to defeat the Gators (7-6) for the third time in the last 13 months.
This one was billed as a Final Four rematch, but both teams limped into the game. UConn had lost five of its previous eight, and Florida had dropped every significant game on its non-conference schedule.
Neither team played much better Saturday. But Boatright and Purvis came up big in crunch time.
Boatright, who missed practice this week while recovering from a thigh bruise, was scoreless in the first 14 minutes. But he made all four of his free throws in the final minute to seal the win.
Florida's biggest issue came from the free-throw line.
The Gators missed 12 of 20 from the stripe. They missed early and really missed late, including all four in the final 40 seconds. They also went more than eight minutes without a field goal in the second half — coinciding with UConn's 10-0 run that closed the gap.
Frazier scored eight points on 3-for-10 shooting. He now has 18 points in the three games against Connecticut.
The Gators led for the majority of the game and were up 44-31 early in the second half. But UConn clamped down defensively and started making shots.
Purvis delivered the key ones. His first 3-pointer made it a four-point game. His second gave the Huskies their first lead of the game. His third put UConn ahead for good.
The Gators went with their ninth different starting lineup this season, with coach Billy Donovan looking for the right combination. At least early, he looked like it found a spark.
UConn: This was the Huskies' first true road game of the season. ... UConn shot 43 percent in the second half and held Florida to 32 percent.
Florida: Guard Eli Carter, returning from a sprained left foot, went 0 for 5 from the field. ... Florida had 15 assists, nine turnovers and seven steals.
UConn plays at South Florida on Tuesday
Florida plays at South Carolina on Wednesday