Harvard had stretched a 28-25 halftime lead to 43-29 on a Wesley Saunders 3-pointer at 13:09.
Malik Gill started a 14-0 run with a layup on the next possession. After Steve Moundou-Missi's layup put the Crimson back up 45-43, Gill's three-point play put the Big Green ahead for good. That started a 12-point burst that put Dartmouth up 55-45 on a Miles Wright 3-pointer with 3:21 to go.
Mitola hit 10 free throws in the final 1:38 to ice the game, running his streak of consecutive free throws to 24.
Dartmouth (8-8, 1-1 Ivy League) lost the first meeting 57-46 two weeks ago.
Saunders and Siyani Chambers led Harvard (11-5, 1-1), which was gunning for a school record 10th straight league win, with 13 points apiece.