The Gators remained the only unbeaten team in Southeastern Conference play, fighting off the Crimson Tide with the help of 17 offensive rebounds.
Florida has not lost since falling by one point at Connecticut on Dec. 2.
Although the Gators could never put Alabama away in the second half, Florida's lead was never less than five points during the final 15 minutes.
Frazier took all 13 of his shots from 3-point range and made five of them. Casey Prather added 14 points for the Gators (16-2, 5-0 SEC). Will Yeguete and Dorian Finney-Smith both had 11 rebounds
Alabama (8-10, 2-3 SEC) was led by 14 points from Trevor Releford.