Cullen had the primary assist on Scott Walker's goal and then helped set up the first of Cory Stillman's two to give Carolina a 2-0 lead in the first period. That goal was originally credited to Cullen, but it was determined in the third period that the puck struck Ranger Jason Strudwick and not Cullen's stick.
It was quite a turnaround for the Hurricanes, who offset an 8-1 drubbing in Buffalo Saturday that kicked off a five-game road trip.
The Rangers squandered a chance to tie Ottawa atop the Eastern Conference standings.
Penguins 3, Coyotes 1 - Kris Letang scored the go-ahead goal off Sidney Crosby's pass midway through the third period and host Pittsburgh edged Phoenix for its fourth victory in five games.
The Penguins got goals from rookies Letang and Tyler Kennedy in the final nine minutes after Shane Doan had tied it early in the third for Phoenix, which went winless on a four-game road trip.
Stars 2, Blue Jackets 1 - Niklas Hagman's shootout backhander powered visiting Dallas over Columbus. Hagman, the 10th player in the shootout, swooped in on goalie Pascal Leclaire and flicked a backhander past him.
Sharks 3, Avalanche 2 - Steve Bernier, Milan Michalek, and Mike Grier scored, and Evgeni Nabokov made 33 saves to lead San Jose over Colorado in Denver.