Abraham scored five points in the final 2:19 as part of a 7-4 run to help Robert Morris (6-7) break a 74-74 tie.
Ohio (8-5) tied the game for the fourth time on two free throws by Kenneth Van Kempen with 2:14 to play.
Abraham was 6 of 7 from 3-point range to lead the Colonials to 60 percent from behind the arc (9 of 15).
Mezie Nwigwe added 11 points, including a free throw with 12:30 left to give Robert Morris its biggest lead, 22-6, with 12:30 left in the first half.
Jay Kinney scored 25 points and Cooper finished with 22 for Ohio.