It's the longest winning streak for Navy (7-2) since 2009.
Penn used a 7-0 run to cut Navy's lead to 57-55 with 2:11 left. Darien Nelson-Henry's free throw with 1:03 remaining pulled the Quakers within one, the closest they came in the second half.
Anderson answered with a layup and hit two free throws with 16 seconds left for a four-point lead.
Abruzzo and Anderson both went 4 of 8 from the field and Abruzzo made all three of the team's 3-pointers.
Despite shooting 50 percent from the field - 57 percent in the second half - Penn couldn't overcome a 12-point halftime lead. Antonio Woods had 16 points on 7-of-13 shooting for Penn (4-3), which turned it over 18 times resulting in 22 Navy points.