Carey Price made 27 saves for the Canadiens (18-13-6), who have won three of their past four games and six of eight heading into the Christmas break.
"We started the game bad, but we all stepped up," said Danault, who scored in a 4-3 loss at the Edmonton Oilers on Saturday. "We played better defensively, and Price] made some big saves. We tied up defensively, and we got better offensively as well. We capitalized, so that was the game today."
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Laurent Brossoit made 42 saves for the Jets (21-14-2), who have lost three of four.
"They were obviously quick," Winnipeg captain Blake Wheeler said. "They hemmed us in a little bit in the second period, (and) we weren't able to get out of our zone. They got a couple good bounces going their way, and all of a sudden you go from having a really good start to being down a few goals, and it's an uphill battle."
Tatar scored his goals 1:32 apart in the first period, tying the game 1-1 on the power play at 15:06 and giving Montreal a 2-1 lead at 16:38.
"I thought we really had a hard time finding our legs in that first 10 minutes, and they were taking the play to us," Canadiens coach Claude Julien said. "It just seemed that the second half of the first [period] we started finding our legs, and I thought we started playing better."
Tatar said, "I think the whole line (with Danault and Brendan Gallagher) is playing really well and clicking. We were clicking last year. We're just trying to work hard and continue to be desperate for the team. I think just because we're talking a lot, it's just working for us right now."