Grand Canyon built a 10-point lead in the first half, going into intermission with a 28-18 advantage.
Transfer Ryan Majerle, nephew of coach Dan Majerle, came off the bench to lead the Antelopes (1-1) with 13 points. Royce Woolridge scored 11 points, hitting 9 of 11 attempts from the line, and Daniel Alexander added 10 points.
The Antelopes were 20 of 45 from the field (44.4 percent) but just 5 of 19 from behind the arc.
Danny Robison, the only Montana State shooter to convert at three-point attempt, finished with 17 points on 5 of 12 shooting from the field and 3 of 7 from long range.
The Bobcats (0-2) were 15 of 43 (34.9 ) from the field and 12 of 23 from the line.