Instead, the goalie was called into action for the first time since suffering a concussion on Nov. 13 when starter Josh Harding was injured during the warm-up.
Backstrom made a smooth transition, turning aside 37 shots in regulation and overtime before teammate Charlie Coyle scored the winner in the fourth round of the 3-2 shootout victory.
"You have to be ready all the time and you never know what's going to happen so you have to find a way to be ready and be at your best," Backstrom said after picking up his second win of the season.
Harding suffered a lower-body injury in warm-up after he slipped on a puck.
Backstrom was returning from his first concussion, suffered after an elbow to the head by Nazem Kadri on Nov. 13 that led to the Toronto forward being suspended for three games. His first full practice was Friday.
Wild backup netminder Darcy Kuemper was on his way to Iowa of the AHL, but was contacted at the Winnipeg airport and whisked to the MTS Centre to sit on the bench in case Backstrom needed relief.
"He (Backstrom is) the difference in the game for us," Minnesota head coach Mike Yeo said. "I mean, obviously I give our players a great deal of credit for dealing with the adversity with what happened at the beginning of the game. It's a little bit easier to deal with it when you see your goalie go out and play the way that he was.
"In the first period, we just weren't good enough by any stretch and he kept us in it and gave a us a chance to continue to find our game and it's a real credit to Backy."
Minnesota moved to 15-5-4 and has won six of its past seven games and is 9-1-1 in November.
The loss extended Winnipeg' (10-11-4) winless streak to four games (0-2-2). It was the Jets' eighth shootout of the season and third loss in the contest. Pavelec stopped 35 in regulation and overtime for Winnipeg.
Aside from Coyle, who deked to beat Pavelec for his first career shootout goal and second attempt, Mikko Koivu also scored in the shootout. Bryan Little beat Backstrom for the Jets.
Michael Frolik and Matt Halischuk each had a goal and assist for Winnipeg in regulation.
Nino Niederreiter and Zach Parise scored for Minnesota, with Parise's 11th of the season sending the game into overtime. Parise added an assist and now has 12 points in his last 10 games.
Jets coach Claude Noel said his team played a pretty good game against the surging Wild.
"They've been the best team in the National Hockey League in the month of November," Noel said. "It's not been an easy task. We've lost to them 2-1, 2-1 and now 3-2 in a shootout so we're close, we're getting there."
This time, the back-breaker for the Jets came in the third period.
Winnipeg was ahead 2-1 and it looked like the lead might be secure when Wild defenceman Marco Scandella was called for hooking at 14:02.
But the short-handed situation was no challenge for the Wild.
Ryan Suter, Mikko Koivu and Parise got on a 3-on-2 breakway and Parise fired a low shot past Pavelec with 4:48 remaining.
"The puck got rimmed around, didn't quite make it to the defenceman and boom, they came back 3-on-2," Noel said.
Pavelec thought his teammates played better, but was lamenting not getting two points.
"The way we lost today, it's disappointing," Pavelec said. "We had the game. We had it. We should close it up. We didn't and we lost the point."
After a scoreless first period in which Winnipeg outshot the visitors 14-4, Frolik marked his sixth goal of the season late in the second when the Wild turned the puck over just outside their blue-line.
Frolik got the puck and sent a pass to Halischuk, who fired high at Backstrom. The puck went into the air and then onto the ice near the crease, where Frolik was on the spot to flip it into the net at 13:07.
Minnesota tied it up 1-1 at 3:21 of the third when Scandella took a pass from Parise and fired a shot from the high slot. Niederreiter got the rebound and put it past Pavelec.
The Jets regained the lead just over two minutes later after Halischuk took advantage of his own rebound to score his second of the season.
Winnipeg had four shots in overtime, with Wild winger Jason Zucker breaking up a 2-on-1 rush as Evander Kane was about to shoot and Devin Setoguchi's low shot stopped by Backstrom. The Wild had one shot on net in overtime.
Winnipeg embarks on a six-game road trip, beginning Monday in New Jersey. Minnesota finishes a four-game road trip in St. Louis on Monday.
Notes: Veteran Winnipeg defenceman Mark Stuart returned to the ice after missing the past 10 with a hip injury.