The Habs had the Rangers cornered late in the third period, but a goal from Chris Drury tied the score at 3-3 and sent the game to overtime.
Brendan Shanahan ultimately took advantage of a giveaway from defensemen Roman Hamrlik to score the game-winner with a precise wrist shot.
Both Andrei Kostitsyn and Tomas Plekanec played well for the Habs, with each contributing to every Montreal goal. Kostitsyn finished with two goals and an assist, Plekanec with a goal and two assists.
Daniel Girardi and Jaromir Jagr scored the first two Rangers goals.
With eight points out of a possible 12 during their year-end road trip, the Canadiens avoided the major slide in the standings that many had expected. The line adjustments made head coach Guy Carbonneau yielded positive results for the team.
Montreal now returns home, where they'll face the Tampa Bay Lightning at the Bell Centre on January 3rd.