Cole scored three goals and the Hurricanes held off the Vancouver Canucks for a 5-3 victory Saturday, ending their five-game skid.
Carolina (6-17-5), which made the Eastern Conference finals last season, has the league's worst record.
"It could have been four or five [goals] tonight," Carolina coach Paul Maurice said of Cole, who missed 10 October games with a broken leg. "I think he has been skating much better. When he skates like that he's a handful, and it opens up the ice for everybody."
Cole's sixth career hat trick was his first multigoal game for Carolina since he was reacquired from Edmonton on March 4.
"We're still a little bit under fire," Cole said. "They weren't just coming at us with three and four guys. They had four and five guys on every rush and pressed us back on our heels. When you've had things go wrong like we've had in the past, maybe it's a little bit easier for something like that to creep back in."
Ray Whitney had a goal and two assists for Carolina, which ended Vancouver's three-game road winning streak. The loss was the Canucks' first in six games against Eastern Conference opposition this season.
"It's huge, especially weathering the storm in the third period," Legace said. "The last couple of games we've kind of shut her down in the third and teams have taken advantage of us."
But Whitney evened the score for Carolina just 20 seconds later, taking a pass from Eric Staal in the left circle and flipping a backhanded shot over Raycroft's left shoulder.
Cole put Carolina ahead 2-1 at 3:55 of the second, taking a snap wrist shot from the slot off a pass from Whitney. Sergei Samsonov made it a two-goal lead at 6:06, beating Raycroft over the left shoulder from the right circle.
Carolina made it 4-1 on a power play at 18:59 of the second, when Raycroft appeared to simply lose the puck out of his glove before it slid across the line. Cole, the last Hurricane to touch it, was credited with his second goal.
Steve Bernier brought the Canucks back to 4-2 at 10:07 of the third, receiving Mikael Samuelsson's pass from behind the goal and across the crease, tipping the puck off Legace's left skate into the net.
"Their top players certainly played a really strong game, but for whatever reason again we had a second period that's tough to explain," Vancouver coach Alain Vigneault said.
Cole scored his third goal into an empty net at 19:46.
Carolina's Aaron Ward collected his 100th career assist on Whitney's goal. ... Scott Walker was back in the lineup for Carolina and started after missing eight games with an upper-body injury. It was the former Canuck's 200th game for Carolina. ... Carolina forward Jussi Jokinen was scratched with a lower-body injury, while Chad LaRose missed his third straight game with a lower-body injury.