D.J. May added 96 yards and a score for Wyoming (1-0), which has beaten Montana in all 14 of their matchups.
Of the 301 total yards gained by the Cowboys in the game, 209 came on the ground during the game, which was delayed twice by lightning for a total of about an hour.
Wyoming's defense held the Grizzlies (0-1) to 253 total yards, including just 42 rushing.
Quarterback Jordan Johnson completed 24 of 45 passes for 185 yards and one touchdown for Montana, a Football Championship Subdivision school.
Bohl was hired last December after leading North Dakota State to three consecutive FCS national championships.
He brings with him a coaching philosophy based on a pro-style, ball-control offense and a stingy defense - completely opposite from the spread offense and porous defense the Cowboys exhibited over the last few years under former coach Dave Christensen.
Wyoming's offense averaged 31.2 points and 472.8 yards per game last year, while the defense gave up 36.7 points and 482 yards a game.
The new offense did its job on Wyoming's first possession of the game, driving 57 yard in 12 plays for a 41-yard field goal by Stuart Williams.
But the Cowboys had two other drives into Montana territory ended by an interception in the end zone and a fumble on a quarterback sack - one of four sacks by the Grizzlies in the first half.
Montana took a 6-3 lead into halftime on a 26-yard TD pass from Josh Janssen to Ryan Burke. The extra point failed.
Wyoming scored both its TDs in the third quarter - a 5-yard run by Wick and a 58-yard run by May.
Johnson connected with Mike Ralston on a 16-yard TD pass in the fourth quarter, but the Grizzlies couldn't muster any more drives against the Cowboys defense.