Brown hit a shot-clocking beating 3-pointer with 1:17 to play to give the Braves a 54-50 lead and a jumper with a half-minute left to make it 56-52.
Aaron Cook made a layup for the Salukis with 21 seconds to go but after Luqman Lund made just 1 of 2 free throws with 19 seconds left, Southern Illinois had a chance. Neither of the final two shots were close.
Neither team led by more than eight points nor shot 40 percent.
Elijah Childs added 12 points for the Braves (9-10, 1-5 Ohio Valley Conference), who ended a five-game losing streak.
Armon Fletcher had 13 points and Cook 12 for the Salukis (9-10, 2-4), who have lost four straight.
