Cal Poly got off to a fast start and held a 10-point lead midway through the first half after David Nwaba's layup with 11:03 left to make it 20-10.
But the Highlanders climbed back by getting players to the basket for layups.
Nwaba got to the basket for a layup to cut the Riverside lead to one, 69-68 with 37 seconds left, but Malik Thames answered by hitting the front end of a one-and-one Jaylen Bland added two more free throws with eight seconds left to seal the victory.
Bland and Secean Johnson each scored 15 points for Riverside (12-11, 3-4).
Brian Bennett scored 21 points off the bench to lead Cal Poly (8-11, 2-4). Nwaba finished with 16 points.