After winning a face-off for Detroit in the Vancouver zone, Dylan Larkin passed the puck from the blue line down to Justin Abdelkader, who one-touched it to Tatar for a quick shot under goalie Jacob Markstrom's blocker from the right circle for his first point in eight games.
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"I just tried to get it out of my mind, trying to play simple but obviously in a big win that feels pretty good, I guess," Tatar said of the milestone. "I feel like in this moment the most important thing for us is two points."
Martin Frk and Darren Helm scored, and Jimmy Howard made 26 saves for the Red Wings (8-7-1), who have won four of five after a six-game losing streak.
"Over the last four games we paid a lot better attention to detail," Howard said. "We're doing a good job on the road of keeping it simple, and when we get our opportunities, we are burying them."
Daniel Sedin and Michael Del Zotto scored for the Canucks 2:14 apart in the third period to tie the game 2-2, but the Red Wings, who were coming off a 4-0 win against the Edmonton Oilers on Sunday, responded with six of the next seven shots before Tatar scored.
"We started playing really good hockey again," Tatar said. "When you have a two-goal lead, you are trying to sit back, play careful. they eventually tied it up, but we just started playing again, started buzzing again."