Octavius Brown added 14 for the Braves (10-15, 7-6 Southwestern Athletic Conference), ending the five-game winning streak of the Golden Lions (9-16, 6-6).
Marcel Mosley had 16 points and Ghiavonni Robinson, who missed a 3 with 2 seconds left, 15 for Pine Bluff.
The Braves raced to a 30-19 lead at the half. But Pine Bluff quickly got back in the game and two free throws by Mosley put Pine Bluff up 38-37 at 10:47. He followed that with a three-point play.
Brown and Hampton hit consecutive 3's to put Alcorn up for good at 50-48 with 3:59 to play. A Josh Nicholas free throw put Alcorn up for good, 51-50 with 2:24 to go.
The game stayed close because Alcorn only made 14 of 26 free throws.