Pointer's layup in transition gave St. John's a 58-53 lead, but Xavier's Jalen Reynolds answered with a dunk and his block on the Red Storm's next possession led to two free throws by Trevon Bluiett to pull within 58-57 with 25.2 seconds left.
Xavier's Remy Abell then picked Harrison's pocket and the Musketeers called timeout to set up their final play. Myles Davis missed a contested jumper and St. John's secured the rebound.
St. John's (19-9, 8-7 Big East) sits in fifth place in the conference standings, a half-game ahead of Xavier (18-11, 8-8).
Rysheed Jordan added 10 points as St. John's won for the fifth time in its last six games.
Bluiett led Xavier with 17 points.