Boynton, who matched his season-high in scoring, had 18 points by halftime as the Gators took a 46-35 lead. Florida held its biggest lead at 83-57 with 4:04 left.
The Gators didn't show any signs of a hangover from its 85-83 double-overtime loss at Rutgers on Thursday.
Boynton, who came into the game averaging 18.9 points, had a big first half making 6 of 7 shots, including 3 of 4 from 3-point range.
Florida took the lead for keeps at 13-12 on a basket by Murphy after Yale started the game by making three straight 3-point shots to grab a 9-0 lead in the opening 2 minutes.
Yale hit 9 of 14 from 3-point range in the opening half to keep the score respectable with the 6-foot-10 Mangano perfect on three tries from long distance. Mangano had 11 points and seven rebounds in the first half.
Both teams shot well from 3-point range. Yale connected on 11 of 21 with Mangano hitting 5 of 7, while Florida was 12 of 21 with Boynton and Murphy each good on 5 of 7.
Florida shot 53.4 percent overall to Yale's 42.9 percent.
Both teams were coming off tough road losses Thursday night. Yale rallied from a 19-point deficit before having a six-game winning streak snapped at Wake Forest.
The Gators blew a seven-point lead in the final 3 minutes of regulation and a three-point lead with less than 20 seconds to go in the first overtime before losing at Rutgers. All three of Florida's losses this season have come on the road, the others against Syracuse and Ohio State, the nation's Nos. 1 and 2 teams. The Gators are 8-0 at home and 3-0 at neutral sites.