Notre Dame (6-2) had a 37-27 rebounding advantage over Delaware (5-4) and outscored the Blue Hens in the paint 36-24. The Blue Hens shot 54 percent in the second half, but couldn't come up with the big shots when they needed it at the end.
Threatt led the Blue Hens with 23 points and Davon Usher and Kyle Anderson had 19 points each.
Grant was 10-of-16 shooting and added four assists, while Connaughton hit 3-of-4 3-pointers, grabbed 11 rebounds and had three steals.
Notre Dame used a 13-0 run late in the first half to open a 42-35 halftime lead, scored the first two baskets of the second half to open a 46-35 lead. Grant later brought the crowd to their feet with a one-handed fast-break dunk on a pass from Eric Atkins to give the Irish a 56-44 lead with 14:15 left.
The Blue Hens later used a 5-0 run to cut the lead 62-56 on a pair of free throws by Devonne Pinkard. Anderson hit a 3 pointer for the Blue Hens with 7:07 left to cut the lead to 68-64. The Blue Hens cut the lead to 70-67 moments later when Anderson missed everything on a 3-pointer, but Usher caught it and scored.
The victory marked the first time the Irish had played Delaware, where Irish coach Mike Brey got his start as a head coach, leading the Blue Hens to a 99-52 record over five seasons before taking the Notre Dame job in 2000.