Wheeler stuffed a rebound under Minnesota goaltender Niklas Backstrom to give him nine goals in 12 games in December after managing five in his first 28 games that included a goalless 14-game November schedule.
Tobias Enstrom scored an empty-net goal at 19:56 to seal Minnesota's fourth consecutive loss. The win broke a two-game losing streak for Winnipeg, which was coming off a 6-2 road loss against the Edmonton Oilers on Monday before the holiday break.
The Wild (20-15-5) are third in the NHL in home wins with 14, but the road has impeded Minnesota from making more of an impact in the standings. It is 6-12-3 on the road after losing all four on this trip. The Wild begin a four-game homestand Sunday against the New York Islanders and play eight of their next 11 games there.
"It's huge," Wild defenseman Ryan Suter said. "We can't win on the road, so we better make sure we play hard at home."
The Jets (17-18-5) won for the fourth time in 18 games against a Central Division opponent (4-11-3). It moved them to within six points of the Wild in the Western Conference Stanley Cup Playoff race and gave them their sixth home victory in regulation through 21 games.
A pair of teams that ranked in the bottom half of the League in scoring combined for five goals in the opening 7:04 and finished the first period with Winnipeg leading 4-3. The Wild, who ranked 29th in scoring with 2.13 goals per game, had nine goals in their past nine road games. The Jets, ranked 18th, put four first-period goals past Backstrom on 11 shots.
"[It is] another reminder," Wild coach Mike Yeo said. "It's not who we are, and it's not how we're going to get it done."
Dany Heatley, Justin Fontaine, Stephane Veilleux and Mikko Koivu scored for the Wild; Jason Pominville has two assists. Evander Kane, Olli Jokinen and Dustin Byfuglien scored for the Jets. Andrew Ladd had two assists, and 13 Jets skaters recorded at least one point.
With Minnesota goaltender Josh Harding out of action, Backstrom made his fourth consecutive start and stopped 32 Winnipeg shots. The Wild chased Jets starter Ondrej Pavelec 7:04 into the game with three goals on six shots. Al Montoya replaced him and made 22 saves.
"The first period was a tough period for everybody involved when you've had three days off," Yeo said. "But [Backstrom] gave us a chance to win that game. I'm not going to say that he didn't play well."
The Wild opened the scoring 2:13 into the game when Byfuglien's defensive-zone turnover allowed Pominville to feed Heatley, who tapped in his eighth goal. Goals from Kane and Jokinen 2:09 apart put the Jets in the lead. Kane scored his 11th, finishing a 2-on-1 shorthanded rush with Michael Frolik 1:35 after Heatley's goal. Jokinen followed with his ninth goal, jamming a rebound under Backstrom's pads.
The Wild pushed back with two goals in 10 seconds, a team road record. Winnipeg center Mark Scheifele's clearing attempt banked off Fontaine's skate into the net at 6:54, breaking his 15-game goal drought after he started the season with six in 18 games. Veilleux followed with his first NHL goal since Feb. 2, 2010, beating Pavelec with a high glove-side shot at 7:04.
"I think you could see the three-day break in both teams," Jets coach Claude Noel said. "There were five goals scored in [7:04], and we made a goalie change that, for me, didn't really have anything to do with Pavelec. I think our team needed the jolt. We certainly couldn't continue to play that way."
Wheeler began the Jets' rally when he tipped his first goal of the game past Backstrom at 14:50 to tie it 3-3. Byfuglien's seventh goal off a scramble in front of Backstrom broke his 15-game goalless streak and moved the Jets into the lead at 17:50, the period's fourth lead change.
"The early goals can be deflating sometimes, and the best part about [the game] is that we found a way to come back," Ladd said.
Minnesota erased that Winnipeg lead 3:40 into the second period when Koivu deflected a shot on its second power play for his eighth goal and a 4-4 tie.
"It is [the] little things right now that are killing us, and [we are] finding ways to lose hockey games," Yeo said of a team that is 3-7-0 in its past 10 games. "Earlier in the year, we were priding ourselves on all of these little things. It's still there. We just have to find it. Our focus is not directed the right way right now."
Yeo looks forward to getting his team back to Minnesota.
"I think coming home is going help, first of all," Yeo said. "We can't just rest on that, for sure. It's just about us building our game first and getting back to that foundation and trusting that if we do that, that the result will come. We're trying to put the result ahead of the process, and that doesn't work."
The win eased some of the pressure on the Jets, who are 5-6-1 in December and have been close to drifting out of contention in the Western Conference.
"It hasn't been an easy month," Wheeler said. "It's been tough. A lot of our guys have been doing a lot of soul searching. Losing hockey games isn't a whole lot of fun. It's not a whole lot of fun to be productive in losses; you want to produce towards wins."