This was also the Blue Devils' second win since being banned from their locker room by coach Mike Krzyzewski last week. Jeff Capel is 3-3 as interim coach for Krzyzewski, who is still recovering following back surgery.
Duke leaned heavily on its starting five, getting all but six points from that group, with Kennard and Amile Jefferson fouling out. The teams combined for 48 fouls and 52 free throws.
V.J. Beachem scored 20 points and Bonzie Colson had 17 points and nine rebounds for Notre Dame (17-6, 6-4), which has lost three straight.
After the Irish cut Duke's lead to six, Jones responded with a three-point play and scored five of the next seven points to push Duke ahead 63-50 with 9:34 left.
The Irish weren't done yet, running off 12 straight points to cut the lead to one with 6:25 to go, but again the Devils responded, with Allen hitting a 3-pointer and a pull-up jumper from atop the key.
That sparked an 11-2 run that again pushed the Devils lead to double digits with 2:29 left.
Duke outscored the Irish 16-4 to end the first half and held them without a field goal for the final 8:41 to take a 12-point lead. Despite being loudly booed the entire game, Allen had 10 points before the break. No player off of either team's bench scored a point in the first half.
Duke: The Blue Devils picked up just their second win against the Irish in the seven games they've played since Notre Dame joined the ACC and have won three of four overall.
Notre Dame: After opening ACC play with five straight wins, the Irish are struggling, losing four of their last five, including a buzzer-beater at Georgia Tech on Saturday.
Duke: A home game Saturday against Pittsburgh kicks off a three-game homestand.
Notre Dame: The path doesn't get any easier in the ACC for the Irish, who head to Tobacco Road to face No. 12 North Carolina on Saturday.