''We had a little something going tonight,'' Schmaltz said. ''We're just trying to stay focused on playing hard away from the puck. If we can get the puck, I think we can have a lot of success.''
Montreal's first trip to Arizona since 2019 pitted the two teams at the bottom of the NHL standings and the league's two lowest-scoring teams.
The teams combined for six goals in the first two periods before shutting each other down in the third.
Travis Boyd and Janis Moser also scored for the Coyotes, who were without coach Andre Tourigny and four players due to COVID-19 protocols. Clayton Keller added an empty-net goal and Karel Vejmelka had 24 saves.
''For us, it is a process to get better every day and to be the best version of ourselves again tonight,'' Coyotes assistant coach Mario Duhamel said. ''We knew that we had an opportunity and we could capitalize on it, which we did.''
Ryan Poehling scored Montreal's second power-play goal in its last 35 chances and Rem Pitlick also scored. Cayden Primeau allowed four goals on 16 shots before being replaced by Sam Montembeault in the third period.
The Canadiens, a Stanley Cup finalist last season, have one win (1-10-3) in their past 14 games.
''When we show up for a couple of periods or a couple of shifts and sometimes we don't,'' said Montreal left wing Jonathan Drouin, who had two assists. ''And that's on the players, not the coaches, not the trainers, it's only the players that have to show up and start playing.''
Montreal arrived in the desert with 19 points, one behind the Coyotes.
The Canadiens had a chance to end their five-game losing streak Thursday in Chicago, but gave up a goal in the third period and another in overtime to lose 3-2.
The Coyotes were blown out 5-0 by Colorado on Saturday, but got off to a rare fast start against Montreal.
Boyd scored early in the first period, gathering a pass from Schmaltz and beating Primeau from the left circle. Larsson scored midway through the first, beating Primeau to the glove side from the left circle on a feed from Phil Kessel.
The Coyotes set up Montreal for a prime scoring chance late in the period, when defenseman Victor Soderstrom coughed up the puck in his own end. That led to a quick 2-on-1 and Pitlick one-timed a pass from Drouin past a sliding Vejmelka.
The goals kept coming in the second period.
Moser scored early in the second, skating around Josh Anderson - back after missing 11 games with a hand injury - and beating Primeau with a backhander.
Poehling gave Montreal its rare power-play goal, redirecting a shot by Drouin past Vejmelka to make it 3-2.
Arizona scored right after a power play late in the second period when Schmaltz gathered a pinballing puck and slipped it under Primeau's glove. The goal was upheld after Montreal challenged for goalie interference.
''They didn't have a ton of chances, but they capitalized on them,'' Canadiens coach Dominique Ducharme said.
Along with Tourigny, Arizona was without G Scott Wedgewood and defensemen Cam Dineen, Anton Stralman and Kyle Capobianco due to COVID-19 protocols. ... The Coyotes played a video tribute to former player Christian Dvorak during a timeout in the first period. Dvorak, who played for Arizona from 2015-21, raised his stick and waved to the crowd. ... Montreal F Tyler Toffoli, who underwent hand surgery on Dec. 11, could be ready to play late in the five-game trip. ... The Coyotes are 4-0-0 when leading after two periods. The Canadiens are 1-21-2 when trailing after two.
Montreal: At Dallas on Tuesday.
Arizona: At New Jersey on Wednesday.
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