Braun also blocked three shots and Russell had three steals. Grandy Glaze had 8 points and 10 rebounds for Grand Canyon (3-0).
The Antelopes started slowly, leading just 13-9 midway of the first half and were up 34-24 at the break. Reginald Johnson made a layup and a 3-pointer as Alcorn State closed to 39-34 with 16:26 left.
Grand Canyon's Boubacar Toure slammed a dunk that started a 24-3 run for a 63-37 lead and the Antelopes coasted home.
Grand Canyon made 24 of 49 (49 percent) from the field while limiting Alcorn to 18 of 60 (30 percent).