This is the 10th time in his career, and 7th time this season that Haws has reached the 30-point mark.
The Cougars trailed by one at the half, 38-37, but outscored the Gaels by 14 over the final 20 minutes.
Haws made four free throws to spark an 8-0 BYU run that gave the Cougars a 56-47 lead and scored nine points in the final five minutes to help seal the victory.
Haws scored 38 points in a win over Pacific Thursday and had 48 in a loss at Portland January 23.
Kyle Collinsworth scored 20 points and grabbed nine rebounds for BYU (15-9, 7-4 West Coast).
Brad Waldow had 25 points and grabbed seven boards to lead Saint Mary's (16-7, 6-4), with Stephen Holt adding 16 points and eight boards. James Walker III added 11 points.
This is BYU's first victory over St. Mary's since joining the West Coast Conference.
The Cougars continue their homestand Thursday night against Santa Clara.