Jonah Travis gave Harvard a 68-62 lead with 3:46 left. Later, Columbia's Maodo Lo and Jeff Coby hit back-to-back 3-pointers to tie it at 68 with eight seconds left.
Saunders finished with 18 points, 16 coming in the first half, for Harvard (17-5, 7-1 Ivy League). Siyani Chambers had 16 and Steve Moundou-Missi 14.
Harvard led by as many as 19 points in the first half and held a 48-31 advantage at the break.
Lo scored 22 points for Columbia (11-11, 3-5) on 8-of-16 shooting. Kyle Castlin had 13 and Cory Osetkowski 11. The Lions scored the opening basket of the game but never led again.
Columbia went on an 11-0 run, with six points by Lo, to cut its deficit to 49-45 early in the second half.