Cantey, who also had 13 rebounds, scored on a layup with time running out after an assist from Desmond Jackson and added a free throw for the Bulldogs (11-11, 8-5 Southwestern Athletic Conference).
The Braves (4-22, 3-11) led 66-62 with 1:12 remaining, but Bo Amusa hit a 3-pointer and then a dunk to give Alabama A&M a 67-66 lead at the 0:15 mark. Amusa finished with 17 points.
Two free throws by Ian Francis put Alcorn State ahead 68-67 with 3 seconds left.
Alabama A&M shot just 21.4 percent (9 of 42) in the first half, which ended with Alcorn State up 39-31 after leading by 15.
A 12-0 run gave the Bulldogs a 52-51 lead with 9:21 to play.
Jamar Ragland scored 17 points and Francis had 11 points and 11 rebounds for Alcorn State.