GLENDALE, Ariz. -- Brendan Gallagher scored 22 seconds into his 500th NHL game, and Carey Price made 32 saves for the Montreal Canadiens in a 4-1 win against the Arizona Coyotes at Gila River Arena on Thursday.
Shea Weber had a goal and an assist for the Canadiens (6-4-2), who scored early in each period of their second consecutive win.
"Those goals at the start of periods are huge," Gallagher said. "It carries over for the rest of the period. For us to start the way we did was huge."
[WATCH: All Canadiens vs. Coyotes highlights]
Antti Raanta made 32 saves, and Jakob Chychrun scored for the Coyotes (7-4-1), who lost for the second time in seven games and were coming off a 3-1-0 road trip that ended with 3-2 overtime win against the Buffalo Sabres on Monday.
"The start was the worst possible. I have to make that save (against Gallagher)," Raanta said. "It's tough when it's 30 seconds and you're trailing. Then you're trailing the whole game and you've been traveling a lot. It takes energy trying to chase the game all the time."
On the Canadiens' first shift of the game, Gallagher jammed a loose puck between Raanta's skate and the right post to make it 1-0.
"It's where you've got to go to score goals," Gallagher said. "These little nights you're going to remember, you want them to be wins, and it's definitely nice for guys to play as well as we did."
Video: MTL@ARI: Gallagher jams puck home at the doorstep
Weber made it 2-0 24 seconds into the second. He scored with a one-timer from the left point after Raanta lost a skate blade in the crease and couldn't recover.
"Start of the first period, (the Canadiens score) seconds in; start of the second period, (they score) seconds in," Coyotes coach Rich Tocchet said. "They're killers. You can't give freebie (goals) up to Carey Price. He's too good of a goalie."
Nick Cousins, who played the past two seasons for Arizona, scored 1:17 into the third period to put Montreal ahead 3-0.
"Obviously, it's fun to score against your former team and especially a big goal there in the third to kind of pad our lead," Cousins said.
"He definitely wanted one," said Nick Suzuki, who set up Cousins in the slot with a one-touch pass.
Video: MTL@ARI: Cousins scores off Suzuki's nice feed
Chychrun scored from the bottom of the left face-off circle off a pass from Phil Kessel to get the Coyotes within 3-1 at 4:47.
Chychrun said Arizona didn't have enough sustained pressure against Price.
"He's obviously one of the best in the League, and you need to play a good game against him," he said. "You have to have a lot of chances to put a few by him, (create) a lot of traffic, and we just weren't doing all of those little things."
Drouin made it 4-1 at 11:03. He hit the puck in the crease after Raanta made the save on Joel Armia's shot on the rush, and it went in off Coyotes defenseman Jason Demers' stick.
It was Drouin's third goal in two games; he scored twice in a 5-2 win against the Toronto Maple Leafs on Saturday.
"That's an area we spoke to our team about, starting strong and finishing strong," Canadiens coach Claude Julien said. "Those last few minutes are always important."
Video: MTL@ARI: Drouin jams loose puck home in crase
They said it
"We wanted to have a good start. They had a long travel day (Tuesday), so you're trying to jump on them." -- Canadiens goalie Carey Price on the Coyotes returning from an East Conference road trip
"A couple of guys just didn't have it, they were sloppy. I don't mind some of the effort, it wasn't that bad. But you've got to be strong mentally. If you don't have it in the (offensive end), be sure you're really good defensively. I thought a couple of guys just weren't there." -- Coyotes coach Rick Tocchet
"It was kind of going against us the whole game. I think the entire road trip was pretty good to us, but we came home and got some humble pie." -- Coyotes forward Derek Stepan
Need to know
Price improved to 12-1-0 against the Coyotes. … Montreal is 3-0-0 against Arizona since the start of last season. … Gallagher has scored five goals in his past eight games. … Weber has 29 points (11 goals, 18 assists) in 44 games against Arizona. ... Chychrun's goal was the seventh by an Arizona defenseman this season. ... It was Raanta's first loss to the Canadiens. He was 4-0-0 in six games.
Canadiens: At the Vegas Golden Knights on Thursday (10 p.m. ET; ESPN+, ATTSN-RM, TSN2, RDS, NHL.TV)
Coyotes: Host the Colorado Avalanche on Saturday (9 p.m. ET; FS-A PLUS, ALT2, NHL.TV)
Video: Weber, Price lead Canadiens past Coyotes, 4-1