The victory was just the fourth for the Big Green (7-18, 3-8) in its last 54 visits to the Palestra.
Two free throws by Mitola broke a 61-61 tie with 1:02 remaining, and his three-point play at the 22-second mark gave Dartmouth a 66-61 lead.
The Big Green led 48-36 after a jumper by Boehm with 15:17 left, but the Quakers (7-20, 4-6) got back into the game with a 10-1 run that included two 3-pointers by Dau Jok. They eventually pulled ahead 57-55 on a jumper by Miles Cartwright with 4:48 to play.
Tony Hicks scored 23 points to pace Penn and Jok added 14 on 4-of-4 shooting, all from 3-point range, plus two free throws.