Niklas Backstrom made that stand up with 37 saves for the Wild (7-10), who also got goals from Martin Havlat and Owen Nolan into an empty net to win for the fourth time in five games. Minnesota won in Toronto for the first time (1-4) since joining the NHL in 2000-01.
The Wild were 2 for 4 on the man-advantage.
"We were an opportunistic group," Wild coach Todd Richards said. "You get on the power play, especially a 5-on-3, you have to score and we were able to score."
Alexei Ponikarovsky and Phil Kessel had goals for the Maple Leafs (3-8-5), who had earned points in seven straight games (3-0-4). Toronto failed to build on the momentum of Saturday's 5-1 win over Detroit.
"We seem to struggle when it's not a Saturday night game at home," Toronto coach Ron Wilson said. "Emotionally, we came out a little flat. We were just content to move along.
"We're not good enough to get full of ourselves after we've had a couple of good weeks. I was a little disappointed in our approach, but more teaching tools for me."
The 4-1 hole after two periods was too much for the Maple Leafs to overcome.
"It's not acceptable and we know that in this dressing room," forward Matt Stajan said. "We didn't play a full 60 minutes and at times we looked really flat. We can't play like that in our own building. We've got to learn from this because these are costly points. Just as we're starting to creep back in past a few teams, it would have been a big two points for us."
Compounding matters, defenseman Mike Komisarek left the game because of a lower body injury after taking just six shifts for 2 minutes, 47 seconds of ice time. There was no immediate word on the severity of his injury.
Trying to give his team a spark midway through the second, Wilson moved Matt Stajan from the fourth line to the first with Kessel and John Mitchell. Kessel ripped a shot off the post on a power play soon after, but that was close as that trio came to scoring.
The Wild took two penalties in quick succession, setting up a three-man skating advantage for the Leafs once they pulled Gustavsson, but Backstrom shut the door until Nolan's empty-netter with 3 seconds left iced it.
"You don't see that too often," Backstrom, who earned his 100th NHL win, said of the 6-on-3. "You can't worry too much. Try to enjoy it. ... I think our three did a good job there."
Minnesota decided the game in the second period.
Given a two-man advantage when Ponikarovsky flipped the puck over the glass for a delay of game penalty, Zidlicky broke the tie when his slap shot from the point got between Gustavsson and the post.
The Wild extended that lead to 3-1, taking advantage of an exhausted Leafs unit left on the ice following an icing call. Antti Miettinen forced a turnover in the corner after the faceoff and sent a pretty pass in front to Koivu, who tipped it past Gustavsson.
Zanon's point shot then hit a couple of Toronto sticks in front and flew past Gustavsson.
Havlat opened the scoring at 17:42 of the first period.
Minnesota's lead lasted just 26 seconds, as Ponikarovsky whipped a shot from the side of the net through Backstrom.
Forwards Jamal Mayers and Jay Rosehill, along with defenseman Garnet Exelby were healthy scratches for the Maple Leafs. ... Wild forward Petr Sykora is out indefinitely after sustaining a concussion Saturday against Dallas. Defenseman John Scott was Minnesota's other scratch. ... Komisarek is in his first season with the Maple Leafs after signing a five-year, 22.5-million deal.