Virginia (22-10) led 12-4 6 1/2 minutes into the game but Florida took over from there, steadily pulling away for an easy win.
The seventh-seed Gators (24-10) advanced to a third-round West Region game Sunday against 15th-seeded Norfolk State, which surprised No. 2-seeded Missouri 86-84 in second-round action Friday.
Florida posted an 8-2 run to close out the first half for a 30-22 lead and Prather ignited a 9-0 run with a 3-point shot and capped it with a layup that put the Gators ahead 45-30 with 14:26 to go.
Prather was good on 6-of-7 shots and Beal, who also had 11 rebounds, made 5-of-8. Patric Young made all six of his shots and finished with 13 points.
Virginia's only player to reach double figures was Mike Scott, who scored 15 points.