Wheeler sped in on a partial breakaway after Carolina defenceman Joe Corvo slipped near the blue line and beat goalie Cam Ward. Wheeler's goal concluded a stretch where the teams scored three goals in a span of 1:03.
The Jets have won the first two games of a five-game road trip after losing three in a row at home.
Earlier in the day, Jets rookie defenceman Zach Redmond had surgery to repair a laceration to an artery in his right leg after a teammate accidentally stepped on him during the club's morning skate.
The injury occurred near the end of practice when Redmond tripped and landed on his back. The teammate then stepped on Redmond with his skate, opening a sizeable wound in Redmond's mid-thigh region — cutting the femoral artery.
Redmond was rushed to the hospital and underwent a three-hour operation, the team said. The Jets added that Redmond was resting comfortably and will be out indefinitely.