Phillip Di Giuseppe, Adam Fox and Mika Zibanejad also scored for the Rangers (35-24-4), who were down 2-0 late in the second. Alexandar Georgiev made 32 saves and New York pulled into a tie with Carolina, two points behind Columbus for the final Eastern Conference playoff berth.
The Rangers have won nine consecutive road games and are 9-1-0 in their last 10 overall.
“We just want to make this thing interesting,” Strome said. “We want to play meaningful games. We’re making these games count. Teams are starting to see us catch them in the standings.
“We have to take care of business like we’ve been doing. We’ve come with a pretty good mindset.”
Max Domi and Tomas Tatar scored for the Canadiens (29-28-9), who dropped to 13-16-6 at home and fell nine points out of a playoff spot. Carey Price stopped 30 of 34 shots in his 11th straight start.
“That’s just a case where we have to be better in the third period,” Domi said. “There’s no real rhyme or reason for why it happens. We just have to be better.”
New York cut it to 2-1 at 18:34 of the second when Di Giuseppe skated hard to the net and deflected Fox’s pass past Price for his first goal of the season. The Rangers then scored four times in the third, including twice in a 1:15 span to take the lead.
After being denied by Price on a one-timer seven minutes in, Zibanejad tied it with his 30th goal of the season on a wrist shot blocker side from the right faceoff dot at 11:06. Zibanejad scored in his sixth straight game, tied for the longest streak in the NHL this season, and extended his point streak to nine.
Strome made it 4-2 on a power-play goal with 4:37 left when he deflected Tony DeAngelo’s point shot. Strome added an empty-netter with 1:33 to play.
“I really liked our third period, from all four lines to our defense corps,” Rangers coach David Quinn said. “I give a lot of guys who were having tough nights a lot of credit because they turned it on in the third.”
The Canadiens dropped to 2-5-2 in their past nine games. They’ve squandered two-goal leads in four straight home games for an 0-2-2 record. They also have a league-worst 10 losses when leading after two periods.
“We just can’t blow a lead like that,” said Tatar, who also had an assist. “We had 40 great minutes and we were really happy with our hockey game. We just dropped it. I don’t think they played any better. We were worried to close the game.
“Something’s got to change.”
Montreal took an early lead on Domi’s 16th goal at 3:12 of the first. He extended his point streak to four games when his cross-crease pass to Tatar went off Fox’s skate and in.
Domi has seven points in six games since failing to get a point in five straight.
That score held up through most of a stoppage-filled period until the teams traded goals in the final three minutes.
Tatar put the Canadiens ahead 2-0 on a mesmerizing breakaway goal. After being sprung by Brendan Gallagher in the neutral zone, Tatar froze Georgiev with a forehand-backhand dangle for his team-leading 22nd goal at 17:01.
With the goal, Tatar tied his career high with 58 points in 65 games. He had 58 points in 80 games last season.
NOTES: Jonathan Drouin missed the game with an ankle injury. … D Xavier Ouellet missed his third straight game with a concussion. … Justin St-Pierre refereed his 1,000th game.
Rangers: At rival Philadelphia on Friday night.
Canadiens: Host the Carolina Hurricanes on Saturday night.
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