Harrison was held to just eight points for the game but connected on a trey with 2:32 remaining to put his team ahead 64-63, and St. John's (10-7, 2-3 Big East) held on to end a two-game losing streak.
He also delivered a key blocked shot down the stretch and Jamal Branch hit two free throws with 7.1 seconds left to seal the triumph.
Jakarr Sampson (17 points), Phil Greene IV (13) and Amir Garrett (11) also reached double figures for the Red Storm.
Eric Atkins paced the Fighting Irish (14-3, 2-2) with 21 points, four assists and six steals.
Notable deaths of 2014 [PHOTOS]