Ohio led by 10 points with a minute remaining, but Isaac Chatman made a 3-pointer to pull Campbell within 78-73 with 24 seconds left. Ohio freshman Jason Preston made 1 of 2 free throws and, after Chris Clemons missed a 3-pointer, Taylor sealed it with two foul shots.
It was Ohio's 500th win in Athens.
Clemons led Campbell (1-2) with 26 points. Chatman added 16 points and Andrew Eudy scored 12.
Clemons, Chatman and Eudy, all starters, each scored in double-figures in the first half. The Fighting Camels led 41-35 after shooting 60.9 percent, including 7 of 13 from 3-point range. Trey Spencer knocked down a 3-pointer with just four seconds left in the half.