Jaroslav Spacek also scored for Montreal, which has won three straight games and will return to Quebec for a three-game homestand starting Wednesday against Pittsburgh.
Alex Auld made 25 saves for the Canadiens, who remained within two points of first-place Boston in the Northeast Division. The Bruins crushed the Senators by a 6-0 count Tuesday.
Brandon Dubinsky scored the lone goal for the Rangers, who saw their three- game win streak halted. Henrik Lundqvist allowed two goals on 38 shots in the loss.
With the score tied 1-1, Pouliot’s ninth goal of 2010-11 put Montreal ahead for good. He hustled down the left-wing side and, from a sharp angle inside the lower circle, and beat Lundqvist high to the near side with a laser wrist shot at the 6:03 mark.
The best chance for New York down the stretch was when newly-acquired Wojtek Wolski hit the post from the left circle with three minutes to go, but the Habs held on for the victory.
The Rangers scored the only goal of the first period at 4:15. Matt Gilroy’s long outlet pass found the stick of Dubinsky along the right side of the neutral zone. He used his speed to beat Montreal defenseman Hal Gill down the near side before he swooped in and lit the lamp with a wrister from a sharp angle near the right post.
With 1:11 remaining in the second, the visitors tied it up.
During an extended period at even strength during which Montreal kept the puck in its offensive zone, Spacek took a shot from the left circle and it appeared to deflect off of traffic in front before the puck barely crossed the goal line. Although both Mathieu Darche and Pouliot were hovering around the crease, Spacek was credited with his second goal of the season and the score was tied at 1-1.
This marked the fourth straight game decided by one goal for the Rangers…Wolski was dealt to the Rangers from Phoenix on Monday in exchange for defenseman Michal Rozsival…Lundqvist was credited with a secondary assist on Dubinsky’s goal, and became the first Rangers goaltender to record a helper in three consecutive starts…Montreal has won three of the last five games against New York overall…Both teams finished 0-for-2 on the power play.