The Gators (15-15, 8-9 Southeastern Conference) led by 14 with 1:58 to play, but missed 8 of 14 from the charity stripe before Eli Carter and Kasey Hill closed it out.
Carter made a pair of free throws with 13.4 seconds remaining, and Hill sank an even bigger one that put Florida up 66-62 with 6.3 seconds to play.
Antwan Space missed a 3-pointer on the final possession with Florida playing not to foul.
The Gators won their second straight after losing six of seven and improved their chances of making the NIT. The Aggies (20-9, 11-6) had been looking to strengthen their NCAA Tournament resume, but instead lost for second time in three games.
Alex Caruso led Texas A&M with 20 points.