Burak Eslik's 3 with 11:22 before halftime gave the Cougars a 20-11 lead, but Grand Canyon proceeded to outscore them 29-10 to take a 10-point halftime lead. Braun and Glaze scored 13 points between the two of them during that stretch.
Braun, named tournament MVP at the Global Sports classic in Las Vegas, knocked down 5 of 8 from behind the arc. Glaze was 7 for 8 from the free throw line and grabbed seven rebounds. DeWayne Russell added 11 points and distributed 10 assists.
The Antelopes were 8 of 16 from long range and collected 17 assists on 28 made baskets.
Eslik finished with 17 points for the Cougars. SIUE (3-9) now has lost nine of its last 11 games.