Alex Barnett had 18 points and Michael Giovacchini scored 12 for Dartmouth (8-10, 1-3), which lost to Penn for the 22nd straight time.
Penn led 60-48 with 9:54 left to play before Giovacchini sparked a 16-3 run to give the Big Green a 64-63 lead. Penn moved ahead 67-64 before two free throws by DeVon Mosley cut the lead to 67-66.
Kevin Egee made one of two free throws for the Quakers with 12.5 seconds left and a difficult six-foot shot by Dartmouth's Elgin Fitzgerald rolled slowly around the rim several times before falling out at the buzzer.
