Alabama A&M closed the first half with a 14-6 run, including 3-pointers by Justin Colvin and Baryn Houston, to lead 32-30 at the break.
Texas Southern (17-12, 14-2 Southwestern) led by 10 with 3:59 to go, but Alabama A&M scored on four-straight possessions, including a 3-pointer and layup by Ladarius Tabb. Arthur Wade's layup tied it at 73 with 1:44 left.
Malcolm Riley made 1 of 2 free throws and Chris Thomas followed with a layup to put Texas Southern back up by three with 19 seconds remaining. Rakiya Battle made two from the line to bring the Bulldogs back to within one.
Gibbs made it a two-point game with a free throw, but Tabb missed a 3-pointer with four seconds to go.
Nicholas West led Alabama A&M (8-18, 7-9 Southwestern) with 16 points.