Keller set up Schmaltz's goal into an empty net at 15:42 of the third period for the 6-3 final.
"We really opened the door there and that was unfortunate, but I think we rebounded pretty well in the third," Coyotes defenseman Anton Stralman said. "We knew they were going to put a lot of pressure on and had the momentum of the game at that point. (Vejmelka) made some keys [saves] in the right times to keep us in early on. … I think we dropped a lot of games like that throughout the season, and tonight, except from a few shifts here and there, we had pretty good control.
Hayton gave the Coyotes a 1-0 lead at 1:57 of the first period when he scored five-hole on a delayed penalty.
Stralman made it 2-0 at 3:52, tapping in Riley Nash's backhand pass off a give-and-go.
Laurent Dauphin cut it to 2-1 at 13:38, scoring from the point on a shot that went off Stralman and Coyotes forward Matias Maccelli.
Nick Ritchie put the Coyotes up 3-1 at 18:34 and Crouse, who scored his first NHL hat trick Monday, extended the lead to 4-1 at 19:49 on a breakaway.
NOTES:Montreal forward Josh Anderson did not play because of a lower-body injury. … Schmaltz has 17 points (seven goals, 10 assists), and Keller has 14 points (five goals, nine assists) during seven-game point streaks. … Keller has 60 points (26 goals, 34 assists) in 60 games, and is the fastest player to reach 60 points in a season for Arizona since Shane Doan (58 games in 2007-08). … Caufield tied Maurice Richard (Dec. 28, 1944) for the third-fastest two goals by a Canadiens player. Peter Mahovlich holds the record at five seconds (Feb. 20, 1971) and Stephane Richer is second with two goals seven seconds apart (Nov. 30, 1987). … Caufield's goals were the fastest pair by an NHL player since Radek Faksa of the Dallas Stars scored twice, eight seconds apart, on Nov. 8, 2017.