James Demery scored eight straight Hawks points down the stretch to make it 66-57 with 3:58 left. Miles had 10 points from there to help Saint Joseph's (17-3, 6-1 Atlantic 10) hold on.
DeAndre Bembry scored 13 points and Demery had 11 for the Hawks, who have won 13 of 14. Miles also had a game-high 12 rebounds.
UMass (8-11, 1-6) used an 8-1 run to get the deficit down to 70-65 on Jabarie Hinds' basket with 45 seconds left. Hinds reached 1,000 career points on the play and finished with 13.