The Bobcats (13-13, 6-6 Mid-American Conference) shot 73.9 percent in the second half (17 of 23) after trailing 22-11 with 8:07 to go in the first half and 32-24 at halftime.
Ohio tied it at 60 on a Baltic layup with 6:16 left, then took its first lead on two Baltic free throws with 5:21 left.
Tied for the fourth time at 65 with 3:02 to go, Cooper and Baltic combined to score the final 11 points for the Bobcats. Cooper hit a jumper, a 3-pointer and three free throws and Baltic made three foul shots. Baltic also had nine rebounds.
Ohio, which scored 25 points off 16 Buffalo turnovers, has won three of four.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.