It was the 22nd straight home Ivy League win for the Quakers (6-12, 1-0 Ivy League), who defeated Harvard for the 12th time in a row.
Brad Unger had 17 points and Dan McGeary added 15, both career highs for the Crimson (6-13, 1-2), playing for the first time in 20 days because of exams.
Harvard trailed throughout most of the game but moved ahead 61-60 on a three-pointer by Jeremy Lin with 5:54 left. Two free throws by Lin gave Harvard a 67-66 edge at the 2:43 mark, but Grandieri scored four straight points before Conor Turley hit a layup with 1:17 left to seal the win.