The Bobcats (2-1) jumped out to a 23-10 lead midway through the first half and led by 12 at half. Valparaiso pulled within four early in the second half, but Ohio surged with an 11-3 run to take a 51-39 lead.
The Crusaders (2-2) would crawl back again, coming back to take a late 72-70 lead on a pair of Jordan Coleman free throws.
Ohio answered with six consecutive free throws, as Ricardo Johnson sank three and Kellogg hit two.
Valparaiso went cold for the rest of the game, missing their last five shots in the final 1:43.
Ohio had four players in double figures, as Johnson and T.J. Hall each had 11.