Manhattan took a four-point lead, 70-66, with 30 seconds left after Rich Williams hit a pair of free throws, but Alex Rosenberg cut it to a one with a 3-point play with 18 seconds left. Tyler Wilson hit the first of two from the line to push the Jaspers' lead back to two but Rosenberg fed Petrasek for the game-winner.
Columbia (6-5) is 15-9 in the series that dates back to the 1917-18 season.
Petrasek finished with 26 points on 11-of-17 shooting from the field, and Rosenberg added 19 points after converting 13 of 16 from the line.
Manhattan (1-6) now has lost four straight, including two conference games.