Ohio (2-0) closed the game on a 25-7 run that featured just one made field goal from Tennessee State.
Keron Deshields' jumper with 9:30 left gave Tennessee State a 58-48 lead. But the Tigers missed their next eight shots until Tahjere McCall's layup with 28 seconds left cut Ohio's lead to 6 points.
The Bobcats took the lead on Gavin Block's 3-pointer with 5:02 left.
Tennessee State (1-1) opened the game on a 14-0 run until Simmons hit a 3-pointer just over four minutes in.
McCall made nine free throws on his way to a team-high 17 points for the Tigers, and Wayne Martin had 15 points and 11 rebounds.