Wheeler added an empty-netter for the Jets, who passed Carolina again to take the lead in the Southeast Division with 34 points. The Hurricanes lost 4-1 to Florida and have 32 points.
Brad Marchand scored for the Bruins, who dropped their second straight and are two points back of Montreal for the lead in the Northeast.
Until the third period, the Bruins had given the Jets a lesson in tight defensive play and it was only Jets goalie Ondrej Pavelec who kept them in the game.
Just eight seconds into the second period, Marchand grabbed a loose puck right beside the Winnipeg net and scored because of a mistake by Zach Bogosian.
The Jets defenseman bounced the puck off the net instead of clearing it behind, Marchand swooped in and was free and clear to slip it past Pavelec from the edge of the crease.
The Jets managed to shut down the Bruins in the first period even though Boston had two power-play opportunities.
The Jets didn't score until 11:44 of the third when Wheeler redirected Bogosian's shot from the blue line past Tuukka Rask on a power play.
Then Kane slammed home Grant Clitsome's rebound to put the Jets ahead at 12:41.
Pavelec finished with 27 saves while Rask stopped 22.
Notes: Despite Boston's edge in the standings over the Jets, their top lines entered the game tied at 30 goals and 70 points apiece. ... The Jets have been keeping it clean, particularly at home. Only Calgary and Minnesota have been short-handed fewer times than the Jets. They've had to kill 88 penalties in total and an NHL-low 29 at home, before Tuesday.