The Hawks (10-19, 4-11 Atlantic 10 Conference) shot 60 percent from 3-point range (9-for-15) and 58.8 percent overall (30-for-51), both season highs. They took the lead for good by scoring 11 straight points early in the second half and Groves hit consecutive 3s during a 15-6 run that gave the Hawks their largest lead at 67-57 with 7:11 remaining.
Tony Taylor's layup with 1:28 left cut the lead to 74-70, but the Hawks made six straight free throws in the final 54 seconds to secure the win.
Joseph Katuka led George Washington (16-12, 6-9) with a career-high 15 points. Taylor scored 11 points and Damian Hollis finished with 10 points.
Idris Hilliard made his first seven shots, six of them coming before halftime, and finished with 17 points for Saint Joseph's. The Hawks shot 64 percent from the field (16-for-25) in the first half, but they also committed 11 turnovers and the Colonials held a 9-0 edge at the foul line to lead 38-37 at halftime.
Garrett Williamson scored 11 points and Justin Crosgile scored 10 for the Hawks, who dropped their first seven conference road games and had shot 50 percent from the field only once this season.