"That's what we wanted to do coming in," Habs captain Brian Gionta said. "They have a lot of offensive power, obviously, that you need to be aware of. We did a good job of handling them."
Gionta's line frustrated Chicago's big names all night. Keith and Kane were kept off the scoreboard, while Toews and Sharp were kept to a shot and an assist apiece.
"It was a good test for us," Gionta said. "We responded right off the bat. We gave them the respect, but not too much. We played them hard, we knew what to expect, we came in with a game plan and stuck with it."
The Canadiens outshot the Blackhawks 38-20 and delivered twice as many hits.
Andrei Markov, who scored both goals for Montreal, including one in overtime, thought the Canadiens played their best game of the season.
"Every time we play against a team like Chicago that's high in the standings, it's a big challenge," Markov said. "And we responded well."
Markov took a deflected pass from Max Pacioretty and found the roof of the net at 1:28 of overtime to beat Corey Crawford and secure the victory for the Canadiens.
"We have to continue the same way," Markov said. "That's our game. We have to try to play that game every night. If you play hard every game like tonight, success will be on your side."
Crawford was otherwise outstanding in net for the Blackhawks, stopping 36 of 38 shots he faced. The 29-year-old missed nearly a month with a lower-body injury and is winless (0-1-3) since his return.
But Crawford made key saves in the first period to preserve the scoreless draw after Chicago ran into penalty trouble, and made an excellent save at the end of the second to keep the deficit at one.
With P.K. Subban in the box for a delay-of-game penalty, a sprawled-out, stickless Crawford robbed Lars Eller from close range with the blade of his skate.
"It was a great play," coach Joel Quenneville said of his goaltender's spectacular save. "He stayed with it. He held his ground well, made a nice skate save. Whatever you want to call what he did ... it was nice to see."
After a few close calls by the Blackhawks to start the second, including Sharp missing an open net high and wide, and Kane hitting the crossbar, Markov broke the deadlock at 12:54 for his fourth of the season.
With 6-foot- 5 Habs enforcer George Parros screening him, Crawford couldn't react quickly enough when Markov's wrist shot flew past his blocker.
"I don't think so, I don't think so," Parros said when asked whether he got his stick on it. "I wish it did. I knew I had a good screen on the goalie, so I just wanted to let it go through me and see what would happen."
Parros often has been left out of the Canadiens' lineup. He suffered two concussions this season and dressed in only 10 games. He finished the game with a shot on net and a plus-1 rating.
"I've been looking for some positivity this year and I finally got some there," Parros said. "It was good to be part of a goal to help our team."
Chicago tied it at 9:22 of the third when Marian Hossa deflected Toews' pass over Carey Price's outstretched pads. Sharp also got an assist on the goal.
Bryan Bickell hit the post to Price's left with just more than a minute to play in the third period before the game was sent to overtime.
Price finished with 19 saves.
"If you looked at statistics before the game, the advantage went to the Blackhawks," coach Michel Therrien said. "But statistics are in the past. What matters to us is tonight's game. We can control the present. We can focus on the present."
The Canadiens have won six in a row against the Blackhawks as the host team. Chicago's last win in Montreal was Dec. 3, 2001.
The Blackhawks had a 10-game point streak snapped after a 3-2 loss to the New York Rangers on Wednesday. ... Parros returned to the lineup, and defenseman Francis Bouillon was a healthy scratch. ... The teams face off again April 9 in Chicago.
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MONTREAL, QC - JANUARY 11: Max Pacioretty #67 of the Montreal Canadiens, controls the puck while being challenged...