The teams combined for seven goals in the opening period, at the end of which Winnipeg had twice come from behind to take a 4-3 lead.
Minnesota tied it with the only second-period goal, that coming from Mikko Koivu on the power play, but Wheeler deflection midway through the third put the Jets back in front.
Tobias Enstrom clinched the victory with an empty-net goal with four seconds to go in regulation.
Wheeler's first goal also came on a tip-in and created a 3-3 tie with 5:10 to go in the opening stanza. Dustin Byfuglien lifted the Jets into the lead three minutes later.
Winnipeg ended a two-game skid and Minnesota lost its fourth straight.
Niklas Backstrom surrendered five goals on 37 shots for the Wild.
Notable deaths of 2014 [PHOTOS]