Stevie Taylor added 10 points for the Bobcats (3-3), who shot 48 percent from the field.
Ohio pushed ahead in the second half when Ndour and Javarez Willis each hit 3-pointers during a 9-0 run to make it 51-42 with 8:23 remaining. Alcorn State (1-7) answered right back with 10-2 surge sparked by Leantwan Luckett and Tyrel Hunt.
The Bobcats buckled down from there, closing the game on a 13-3 run in the final 4:47. Campbell hit two layups, Ndour dunked and Ohio finished 5 of 6 from the line during the late surge.
The Braves were held to 19-of-56 shooting (33.9 percent) and committed 16 turnovers. Luckett finished with 15 points, Marquis Vance added 12 and Hunt had 10 with eight boards.