Alexei Emelin scored for Montreal, which held a 2-1 series lead before losing three in a row, including 3-2 in overtime in Game 5 on Thursday. Carey Price made 20 saves.
"It was a close series, so the undoing is probably the fact that it ended up that they scored more goals than us because they were all one-goal games in all of the wins," Canadiens coach Claude Julien said. "We tried everything we could to score and we face a goaltender that is probably, without a doubt, their best player, and we couldn't manage to get those goals.
"It wasn't from lack of trying. We looked at our scoring chances and we looked at it after games and we probably had more than the other team, but they made the most out of theirs. The undoing was the fact that we probably needed a little luck to go with our efforts, and those two combined sometimes gives you the breaks that you're looking for. It was a tough series, but it was a series where I really thought our players worked hard and competed as hard as they could."
Zuccarello tied it 1-1 when he scored the Rangers' first power-play goal of the series at 2:26 of the second period. With Jordie Benn in the penalty box for holding, Zuccarello took a shot from the right circle that squeaked past Price short-side.