Rahamanh Katumbusi's 3-pointer to start the third overtime put the Braves up 84-81 and they never relinquished the lead.
At the end of the second overtime, Alcorn State (5-11, 3-2 Southwestern) got a steal and breakaway dunk from Patrick Onwenu with 21 seconds left to tie it at 81. MVSU (2-16, 2-2) turned it over but Marquis Vance missed a 3 at the buzzer.
Vance tied it at 74 with a free throw with 31 seconds left at the end of the first overtime.
MVSU held a commanding 40-27 lead at the half, but Alcorn State began chipping away and tied it at 62 with an Onwenu layup with 2:49 to play in regulation.
The Braves led 67-64, but Brown fouled Isaac Williams on a 3-point attempt and he sank all three free throws with 32 seconds left.