Cullen, who opened the scoring with his eighth goal midway through the first, gave New York its third and final lead with 6:05 remaining when he once again fired a hard wrist shot past goalie David Aebischer into the top of the net.
Sheldon Souray scored Montreal's third power-play goal 8:40 into the third to tie it at 3. Souray, who has scored 11 of his 14 goals with the man advantage, got his own rebound and drove a second slap shot past Henrik Lundqvist as Montreal drew even for the second time.
Lundqvist made 21 saves for the Rangers, whose winning streak has come after a seven-game skid, New York's longest losing streak since late in the 2003-04 season.
DEVILS 3, SENATORS 2
In Ottawa, Brian Gionta scored twice and the New Jersey got strong goaltending from Martin Brodeur in a victory over Ottawa.
Zach Parise also had a goal for the Devils, but it was Brodeur's nearly flawless performance that made the difference.
Brodeur stopped 33 shots to prevent the Senators, who had won five of six, from earning at least one point for the first time in seven games.
Scott Gomez added a pair of assists for New Jersey.
Ray Emery made 26 saves for Ottawa, but the Devils won their second game in a row and fifth in six tries.
Their only loss during that stretch came in a shootout against the New York Rangers.
Patrick Eaves ended a personal scoring drought with a goal for Ottawa, and Tom Preissing also scored.
BRUINS 4, FLYERS 3
In Boston, Marc Savard had two goals and assisted two others, helping Boston avoid its longest losing streak of the season.
Glen Murray scored his 20th goal of the season for Boston, his fifth consecutive season with 20 or more. Patrice Bergeron had the other goal for the Bruins, who lost their last three games by a combined score of 20-3.
Sami Kapanen scored twice for Philadelphia, which had won three of its last four games.
Mike Knuble scored for the Flyers with 1:55 to play after they pulled their goaltender, but the Flyers had trouble getting the puck past center ice after that.
Bruins defenseman Zdeno Chara missed a game for the first time this season with a lower body injury.