Alcorn State's Kendrick McDonald answered with a 3-pointer with 4 seconds left but it wasn't enough.
The Tigers (4-18, 2-8 Southwestern Athletic Conference) trailed 53-40 with 12:32 to play, and went on an 18-4 run to take their first lead since the 9:06 mark of the first half. Qualls' three-point play put Grambling State up for good, 58-57, with 3:17 remaining. The Braves (3-17, 3-7) committed three turnovers and shot just 2 of 10 from the field during the spurt.
The Tigers trailed 35-28 at halftime, but outrebounded Alcorn State 25-11 and got 14 points and 11 rebounds from Justin Patton in the second half. Patton finished with 22 points and 17 rebounds.
Marquiz Baker led Alcorn State with 16 points.