Montana (9-4) plays at Big Sky Conference foe Eastern Washington next weekend.
The Grizzlies dominated San Diego (9-3) from the start, taking a 38-0 halftime lead and limiting the Toreros to one first down before the break.
Johnson threw first half touchdown passes of 22 and 30 yards to Jamaal Jones and 3 yards to Jordan Canada. Canada also scored on a 17-yard touchdown run and John Nguyen returned a punt 60 yards for a touchdown.
Priest added a second touchdown for the Toreros on an 11-yard pass from Trey Wheeler with 2:48 left in the fourth quarter.