Gillislee's 12-yard scoring run early in the fourth quarter erased a 17-13 deficit and put the Gators (2-0, 1-0 SEC) ahead to stay.
The running back also scored on a 4-yard run on Florida's first drive, finishing with 83 yards on 14 carries for the game.
Gators quarterback Jeff Driskel tossed for 162 yards, completing 13 of 16 attempts.
Florida's win came in the first-ever SEC contest for Texas A&M (0-1, 0-1) which joined the conference after 16 seasons in the Big 12.
Redshirt freshman Johnny Manziel connected on 23-of-30 passes for 173 yards and added a rushing score for the Aggies, who fell in their first game under new head Coach Kevin Sumlin.