It was the fifth straight game with at least 20 points for Haws, tying him with Danny Ainge, Kresimir Cosic and Michael Smith for the second-longest streak to start a season in school history. Devin Durrant scored 20 or more in seven consecutive games to start the 1983-84 season.
The Cougars (3-2) shot 31 of 60 (51.7 percent) from the floor and enjoyed a 48-21 rebounding edge in bouncing back from two losses at the Coaches vs. Cancer Classic in Brooklyn, N.Y.
Trailing 48-28 at the break, UTSA whittled the deficit to 13 with 10:42 remaining. But BYU pushed the lead back to 17, then put the game away with a 9-2 run fueled by Haws, who had five points during the surge.