Phillip Danault had a goal and two assists, Shea Weber had a goal and an assist, and Carey Price made 26 saves for Montreal (11-5-3), which has won three straight and is 7-1-1 in its past nine games.
"I think the whole game was a lot of fun," said Tatar, whose four points were an NHL career high. "We played a strong game, played the right way, and we're happy with these two big points. Obviously, they're a really strong team and that's just a good effort from four lines."
WATCH: [All Canadiens vs. Capitals highlights]
Alex Ovechkin and Evgeny Kuznetsov scored, and Ilya Samsonov made 35 saves for Washington (14-3-4), which lost in regulation for the first time since Oct. 14 (11-0-2 during streak).
"We didn't execute our wall plays, we made lots of turnovers in neutral zone, and it just cost us the game," Ovechkin said. "We know we have to and we can play better. You saw it, guys. We know it. It's our fault."