Wesley Saunders added 18 points while Laurent Rivard and Christian Webster tallied 16 apiece.
Harvard (12-6, 4-0) led 69-64 with 20 seconds left before Sean McGonagill hit a 3-pointer with 14 seconds left, then converted a jumper at the buzzer to send the game into overtime.
Brown (8-10, 2-2) fell behind 78-75 with 38 seconds left in the first OT, but Stephen Albrecht connected on a trey to knot it and send the game into the second overtime.
Harvard outscored Brown 11-4 in the second overtime to seal the victory. The Bears missed three straight 3-pointers over the final 21 seconds of the second extra frame.
McGonagill paced Brown with 20 points and played all 50 minutes of the contest.