Wilbekin hit a baseline floater, Prather followed with his first of two spinning layups and then Florida (11-2) went ahead for good on Young's three-point play.
Dorian Finney-Smith's 3-pointer gave the Gators some cushion down the stretch, and they closed it out from the free throw line -- barely.
Florida missed six of eight free throws in the final minute.
Young finished with 15 points for Florida, which won its 23rd consecutive home game. Prather had 12 and Wilbekin added 10.
Cedrick Lindsay led the Spiders (10-5) with 19 points, and Kendall Anthony added 15.
Florida didn't play particularly well, shooting 26 percent from 3-point range, turning the ball over 14 times and managing just 10 assists. But coach Billy Donovan's team used its experience and leadership to escape with another home win.
The Gators need one more home win -- they open Southeastern Conference play against South Carolina on Wednesday night -- to match the school record of 24 set between 2006 and 2007.
The latest one was in doubt midway through the second half.
Richmond made six 3s in the second half, including five by Lindsay. Lindsay answered consecutive 3s by Frazier with 12-plus minutes remaining with a shot from the wing. He drained another one that put the Spiders up 41-38. Richmond was up 46-42 with 8:34 remaining, but Frazier's third 3 sparked the comeback.
Florida's seniors did the rest.
Prather's second spinning layup resulted in a three-point play and put Florida ahead 55-50.
The Gators used that momentum on the other end, ratcheting up their defensive effort. Richmond fouled repeatedly in the closing minutes, but couldn't take advantage of Florida's misses.
Florida shot 44 percent from the field despite going 5 of 19 from behind the arc and really handled Richmond inside. The Gators outrebounded the Spiders 44-22 and outscored them 38-20 in the paint.
Donovan's team has won five straight and 10 of 11 -- the only loss a buzzer-beater at then-No. 12 Connecticut. So this was another quality win for Florida's non-conference schedule.
Richmond, meanwhile, lost for the first time in regulation since Nov. 23. The team's last two losses -- to Wake Forest and Ohio -- came in overtime.