Prather knocked down two free throws with 28 seconds to play to give the Gators (8-2) a 77-73 edge that held up in the final seconds of the contest, which was part of the Jimmy V. Classic at Madison Square Garden in New York City.
Dorian Finney-Smith added 14 points off the bench for Florida. Scottie Wilbekin and Michael Frazier both scored 11.
Joe Jackson led Memphis (7-2) with 17 points. The Tigers had five players in double figures, but were unable to extend their winning streak past six games.
Florida led 41-38 at halftime and took advantage of a Memphis cold spell to build a 69-61 lead with 6:03 to play.