Bowers led the Tigers (19-7, 8-5 SEC), who remained undefeated at home and snuffed out the Gators (21-4, 22-2) three-game winning streak.
Jabari Brown added 12 points for Missouri and Phil Pressey scored seven points and notched 10 assists.
Mike Rosario led Florida with 14 points and Kenny Boynton scored 11. Boynton had two 3-point tries after Bowers' jumper gave Missouri a 61-60 edge but missed on both.
Florida led 29-26 at halftime but was outscored 37-31 in the second half. The Gators were 6-for-12 from the free throw line while Missouri went 12-for-15.