George Washington (9-1) trailed 41-32 with less than 14 minutes remaining but went on an 18-3 run over the next six minutes to take a 6-point lead.
Savage then scored 11 points -- seven on free throws -- over the final 6:41 to help the Colonials seal the win. Savage finished 11-for-15 from the free throw line while McDonald hit 10 of 12 free throws.
Boston (6-4) shot 6-for-10 on 3-pointers in the first half en route to a 32-24 halftime lead but shot just 39.3 percent from the field for the night. D.J. Irving led the Terriers with 23 points.
The Colonials also struggled from the field and found success from beyond the arc, shooting 39.6 percent but going 6-of-13 on 3s.
Shooting guard Jaylen Nowell, ranked No. 45 in the ESPN 100, chose the Washington Huskies on Wednesday over California. As a junior he led Garfield Heights to a state championship and was named MVP of the tournament.
Donnie Tyndall has filed an appeal to reverse the 10-year show cause penalty he received from the NCAA in April for violations that occurred while he was coaching Southern Mississippi.
Top-50 prospect Jaylen Nowell committed to Washington on Wednesday. Nowell, a shooting guard, is No. 45 on the ESPN 100.