Harvard (14-5, 4-1 Ivy) took the lead for good on Saunders' free throws with 3:04 left. He pushed the lead to five on a 3-pointer 45 seconds later.
Brown (9-13, 0-5) had the ball only once with the score within one possession but Cedric Kuakumensah missed on a layup with the Bears trailing 71-68.
Saunders also forced overtime when he put back his own miss with one second left in regulation, tying the game at 64.
The victory keeps Harvard one-game behind league-leading Yale in advance of a showdown with the Bulldogs on Saturday.