Harrison was 8 of 13 from the field. James Woodard added 21 points for Tulsa (6-3).
The Golden Hurricane made their last field goal when D'Andre Wright made a layup with 6:29 left. Tulsa had its largest lead, 86-62, with five minutes remaining following four free throws.
The Gaels missed three shots, and Tulsa made four free throws to seal it.