Henry scored six-straight DePaul points during its 21-6 burst to open the second half for a 45-41 lead. Western Michigan ended its five-minute dry spell on Drake LaMont's free throws with 7:52 remaining.
Thomas Wilder hit two free throws to get Western Michigan within 53-51, but Garrett scored the next six to extend DePaul's lead to 59-51.
Tommy Hamilton IV had 11 points and seven rebounds for DePaul, which was just 2 of 15 from 3-point range but made 25 free throws.
Tucker Haymond led Western Michigan with 24 points and Wilder finished with 16.
Western Michigan went on a 10-0 run in the first half to build a 28-19 lead and extended it to 35-24 at halftime. The Broncos were outscored 45-28 in the second half.