Brian Grandieri led the Quakers with 19 points, while Harrison Gaines scored 11 of his 16 points in the second half as Penn narrowed a 21-point deficit to eight points before Harvard iced the game with free throws.
Down 67-48, Penn (10-16, 5-4 Ivy League) pulled within 74-66 with four minutes to play. But Harvard, which went 25-of-27 from the free throw line overall, made 13-of-14 free throws in the last 2:39.
Penn's Tyler Bernardini, averaging a team-high 13 points, picked up his third foul a minute into the second half but scored nine of his 12 points in the last 12 minutes before fouling out with under a minute to play.
The Crimson shot 60 percent in the first half while holding Penn to 33 percent to take a 45-28 halftime lead.