The Canes trail the Jets 2-1 after two periods as Blake Wheeler has both Winnipeg goals and Elias Lindholm has a power-play score for the Canes.
The Canes fell behind 1-0 in the first after another sluggish start as Winnipeg played a quicker, more energetic game.
The Jets came into the game off a 3-0 loss in Montreal and ranked 29th in the NHL in scoring at 1.75 goals per game. But Wheeler's tip of a Mark Stuart shot got past Canes goalie Cam Ward at 5:29 of the first.
The Canes tied it 1-1 early in the second after Ward made a sharp stop on a Mathieu Perreault shot. Zach Bogosian was called for hooking and the Canes scored in 30 seconds as Lindholm's shot from the shot of the net glanced off defenseman Mark Stuart and past goalie Michael Hutchinson.
Digital Access for only $0.99
For the most comprehensive local coverage, subscribe today.
The Jets reclaimed the lead at 13:07 of the second on a near repeat of Wheeler's first-period score. Wheeler again gained position in front of Ward and got a piece of the puck on Bogosian's outside shot.
The Canes killed off a Jets power play late in the second to keep it a 2-1 game. Ward has 25 saves through two periods, keeping the Canes in the game.
The Canes managed just six shots on goal in the first -- only two in the first 11 minutes -- to make things simple for Hutchinson. Ward, who has won his last five games, was forced to make a handful of scrambling stops to keep it a 1-0 game.
Zach Boychuk, who scored the Canes' first goal in the 4-1 win Monday over Calgary, nearly gave Carolina a quick lead. Open on the left wing on a rush into the offensive zone, Boychuk was wide with a shot off a cross-ice pass from Brad Malone.
Just after Wheeler's first score, the Jets forward was called for goaltender interference as he crashed the net and bumped into Ward. The Jets, third in the NHL in penalty killing, held the Canes without a shot on the power play.
Ward then made a hustling pad save on a Paul Postma shot to deny the Jets on a three-on-one rush. A couple of minutes later, he stopped a heavy shot by Matt Halischuk.
Hutchinson was making his first start since shutting out the Chicago Blackhawks 1-0 on Nov. 2.