The Fighting Irish hit 12 3-pointers, including four during a two-minute stretch midway through the second half that helped Notre Dame (1-0) start to pull away from the Blue Demons (0-1).
Senior Bonzie Colson, an All-American, finished with 18 points and 13 rebounds, and Matt Farrell added 15 points for the Irish, who improved to 18-0 in season openers under coach Mike Brey.
Tre'Darius McCallum and Eli Cain each scored 14 points to lead DePaul.
The Irish scored the game's first five points and led for almost all of the first half, but never by much. A layup by Cain tied the score at 22-22 with 4:22 left before halftime.
Gibbs hit a late 3-pointer and Notre Dame took a 29-25 lead into halftime.
The Fighting Irish extended the lead midway through the second half. Gibbs hit a pair of 3-pointers, and Rex Pflueger and Farrell also knocked down deep balls to push the lead to 60-47 with 7:46 left.
DePaul returned four starters from last season's team but is picked to finish 10th in the 10-team Big East in the preseason coaches' poll.
NOTES: Saturday's game was the first at Wintrust, DePaul's new home arena after 37 years at Rosemont Arena. ... The Fighting Irish debuted their new Golden Dome uniforms. ... Five of Notre Dame's first seven games are away from home, a stretch highlighted by a showdown at No. 2 Michigan State on Nov. 30. ... Saturday's game was the 105th meeting between Notre Dame and DePaul. ... Notre Dame coach Mike Brey is 18 wins away from reaching 500 career wins.