Thompson made 6 of 7 shots and delivered seven assists. McDermott contributed a team-high seven rebounds.
Baldwin picked up two fouls in the first 3-plus minutes of the game and was limited to 11 minutes in the first half. The senior guard finished with three fouls.
The Bulldogs shot 52% percent while holding the Gators to 44%. Butler made 9 of 20 3-pointers while Florida was 6 of 21. Each team had 10 turnovers.
The Gators, who trailed by nine at halftime, narrowed the deficit to six points twice before the Bulldogs pulled away. Butler's largest lead was 19 points at 61-42 with 7:33 remaining.
Butler finished the first half with a 19-5 run to take a 35-26 lead at halftime. Trailing 21-16, the Bulldogs had an 11-0 run.
Butler owns the nation's longest streak of consecutive non-conference home victories at 56.
Florida: After a solid start on the road, the Gators' four-game winning streak end with a thud. Entering the game with a 30% average from 3-point range, Florida shot 23%.
Butler: The Bulldogs won their third meeting with an SEC opponent in the last four games, previously beating Missouri 63-52 in the Hall of Fame Classic on Nov. 24 and host Mississippi 67-58 Tuesday.
Florida: Home game against another Big East opponent Providence on Dec. 17.
Butler: Travels to No. 18 Baylor on Tuesday.
No. 12 West Virginia looks to rebound at home vs. Texas
The travails and challenges of playing on the road in the Big 12 Conference caught up with No. 12 West Virginia on Saturday, and the Mountaineers will look to rebound when they host Texas on Monday in Morgantown, West Virginia.
No. 2 Baylor seeks 'A' game versus Oklahoma
It didn't take long after No. 2 Baylor rallied to knock off Oklahoma State on Saturday for Bears coach Scott Drew to turn his attention to the next Big 12 Conference matchup.
Baylor jumps Gonzaga to take over top spot in AP Top 25
Baylor and Gonzaga were the only two teams in the top five that took care of business last week.