The Quakers (6-10, 1-1 Ivy) saw most of their 13-point second-half lead erased when Alex Mitola hit a 3-pointer for Dartmouth (8-9, 1-2) with 1:35 left, cutting the margin to 54-51.
Antonio Woods scored the last four points to seal it for Penn.
Penn was first to shake off a sluggish first half that ended with the Quakers leading 20-16. They opened the second with a 13-5 run to go ahead 33-21 on Tony Hicks' jumper with 15:38 left and stretched to their largest lead at 43-30 on Hicks' basket with 8:20 left.
Hicks and Woods added 11 points each and Greg Louis 10 for Penn.
Malik Gill had 15 points, Gabas Maldunas scored 14 points and Connor Boehm 10 for Dartmouth.