Cooley also had 14 rebounds and Grant scored 15 of his points in the second half when the Irish (17-8, 9-3 Big East) finally broke away from the Blue Demons.
The score was 68-all when DePaul's bench was charged with a technical foul. Notre Dame scored the next seven points to go up 75-68 with 5:30 to play.
DePaul (11-13, 2-10) got within three points twice in the final 3:28 but couldn't come closer than that.
Notre Dame outrebounded DePaul 33-21 and shot 60 percent from the field.