But Kentucky scored 13 of the next 15 points to go ahead 47-45. The Wildcats took the lead for the first time since early in the game when Rajon Rondo threw a behind-the-back pass to Ravi Moss for a lay-in with 13 minutes left.
The Wildcats went ahead for good at 53-52 on Azubuike's 3-pointer with 9:52 left and held the lead thanks in good measure to the play of Rondo, their freshman point guard.
The 6-foot-1 Rondo had 14 points, seven rebounds and four assists. He also helped shut down Anthony Roberson, the SEC's second-leading scorer, in the second half when he had eight mostly meaningless points after getting 15 in the first half.
Rondo, a 50 percent free throw shooter, even went 8-of-10 from the line. Kentucky, which entered the game shooting 65.8 percent from the line, went 18-of-24 (75 percent) against the Gators.
Kentucky only had three second-half turnovers after committing eight in the first half.
Kentucky led 64-54 after a three-point play by Azubuike with 3:37 left. Florida came within four points with a minute left and had two chances to pull closer, but Matt Walsh and Roberson each missed 3-point attempts.
Chuck Hayes, who had 11 points and nine rebounds, made two free throws for Kentucky with 26 seconds left and Moss went 1-of-2 from the line with 10 seconds left.
Walsh scored 18 points for Florida. The Gators, who outrebounded Alabama by 25, were outrebounded 34-27 by Kentucky.
Led by Roberson, Florida shot 54.2 percent in the first half and took a 36-29 lead.