Eric Atkins had 17 points and 10 rebounds in the Big East opener for the Irish (13-1, 1-0 Big East).
The victory extended Notre Dame's winning streak to 11 games and gave the Irish 10 wins over Seton Hall (12-3. 1-1) in their last 11 meetings.
Fuquan Edwin and Aaron Cosby scored 21 points each to lead the Pirates, who had won seven in a row prior to Saturday's meeting.
Seton Hall held a 13-11 lead early in the game but Cooley sank a layup with 11:01 to play in the first half that gave Notre Dame the lead for good.