Landry also pulled down 11 rebounds for the Lumberjacks (11-6, 3-1 Big Sky) while Wilson had a game-high eight assists.
Matt Martin had 15 points to pace Montana (6-9, 0-2), which has now lost seven of its last eight.
Montana led 35-26 at halftime but Northern Arizona went ahead to stay at 57-55 on Landry's off-balance jumper with 5:20 remaining.
Landry then made six free throws in the final 1:06 to seal the victory.
The Grizzlies had beaten the Lumberjacks in their last two meetings in Flagstaff- in the regular-season finale last year and in the 2006 conference tournament title game.
Strait made all 11 of his field goals in a game here last season but was just 5-of-7 from the floor on Thursday night.
Staudacher's 3-pointer with 10:20 left in the first half capped an 8-0 run to give Montana a 12-point lead.