Wheeler added an empty-netter for the Jets (16-12-2), who leapfrogged past Carolina again to take the lead in the Southeast Division with 34 points. The Hurricanes lost 4-1 to Florida and are two back.
Brad Marchand scored the lone goal for the Bruins (19-6-3), who dropped their second straight and sit two back of Montreal for the lead in the Northeast.
Until the third, the Bruins had given the Jets a lesson in tight defensive play and it was only Jets' netminder Ondrej Pavelec who kept them in the game.
Just eight seconds into the second Marchand grabbed a loose puck right beside the Winnipeg net and scored thanks to a mistake by Zach Bogosian.
The Jets defenceman 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.
Their penalty kill never wavered but pucks weren't going in until the 11:44 mark 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 before the Bruins had time to recover.
Pavelec finished with 27 saves while Rask stopped 22 at the other end.
The Jets also are one team that matches up pretty well on defence with the Bruins' Zdeno Chara, an imposing six-foot-nine and 255 pounds.
Lined up across the rink is Winnipeg's six-five, 265-pound Dustin Byfuglien. Coincidentally, both wear No. 33.
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 shorthanded fewer times than the Jets. They've had to kill 88 penalties in total and an NHL-low 29 at home, before Tuesday, that is.