Elgin Fitzgerald had 10 points for Dartmouth (7-16, 5-4 Ivy League), which defeated the Quakers twice in the same season for the first time since 1958-59. The Big Green was a 63-60 winner on Jan. 31.
Dartmouth never trailed and built a 54-41 lead with 11:09 remaining. Penn then went on a 14-4 run, closing within 58-55 with 4:20 remaining, before Rufful hit a 3-pointer at the 3:58 mark.
After Penn closed within 61-57, Barnett hit four consecutive free throws to seal the victory.
The Big Green held a 35-26 advantage at halftime, hitting 15 of 31 shots, while Penn was 10 for 23 with eight turnovers.
The victory was Dartmouth's first at Penn's home court, the Palestra, in 11 years.