John Baumann had 23 points and 13 rebounds for the Lions (8-11, 1-3 Ivy League), who have lost four in a row.
Baumann scored 16 points in the first half, but the Bears (10-8, 2-2) fronted him in the second half with either Matt Mullery or Scott Friske instead of playing behind him. As a result, he had just seven points in the second half, five in the final 32 seconds.
Columbia led 35-34 at halftime but Brown went on a 14-3 run to open the second half and built a 48-38 lead. Sullivan and Adrian Williams, who finished with 12 points, each scored five points to key the run.
The Lions pulled within five on two occasions, the last at 65-60 with 32.3 seconds left. But Brown clinched the victory at the free throw line when Williams made the front end of a one-and-one and Sullivan connected on both ends.