The Maple Leafs, who won their third in a row, were outshot by the Wild 38-14, but Toronto took an early lead on Tyler Bozak's power-play goal 4:24 into the first period. Bozak connected on give-and-go passes from Cody Franson and Dave Bolland that caught the Wild defense out of position.
"Special teams can win and lose you games," Bozak said. "It's something we got really good at last year and we're happy we've been able to keep that trend going."
Minor-league call-up Trevor Smith scored his first with the Maple Leafs on a lead pass from rookie Morgan Rielly. Smith's shot trickled through Wild goalie Darcy Kuemper's five-hole to give Toronto a 2-0 lead at 13:51.
A power-play goal by Minnesota forward Jason Pominville at 17:27 cut the lead to 2-1, but in the second period, Raymond scored a power-play goal, using a nifty move to beat Kuemper at 12:23.
The goal came on Toronto's seventh shot and forced Kuemper out of the game in favor of Josh Harding.
"Their front [defense] was definitely pressuring up the half-wall and [Kadri] made a good pass," Raymond said. "You want to take pucks to the net, and our special teams have been key, and that was another big goal for us."
For 23-year-old Kuemper, it was his seventh start in the NHL. He was pressed into duty Tuesday because of Niklas Backstrom's injury and Harding's start Monday night against the Buffalo Sabres.
"[I told him] just to keep his head up," Wild coach Mike Yeo said of Kuemper. "I feel bad for the kid. First off, in fairness to him, that's a tough situation for a young goalie. I don't think he saw his first shot till the 12-minute mark and then it's a bang-bang play [and] it's in the net.
"We're not pinning this on him by any means. It was a tough situation for a young goalie and he'll get a chance to bounce back."
"You come out and try to take away the angle and wait for him to make a move," Reimer said. "He kind of pulled it, and I thought he might try and [put it over my shoulder], but then he pulled to his backhand and tried to slip it in five-hole. It's a really good move; it's just my stick happened to be there and I was lucky enough to make a save."
In the third period, Toronto would hang on while Minnesota provided more pressure, but Reimer shut down the Wild attack, stopping 36 shots overall. Raymond added his second goal into an empty-net at 19:02.
Reimer's win was his first since opening night of Toronto's season. He had 10 days off between starts serving as Jonathan Bernier's backup.
"We know both our goalies are great goaltenders," Bozak said. "James has been doing it here for a long time, giving us a chance to win every time he plays, and obviously [Bernier] this year has been doing the same thing. Whichever one of them is in net, we're pretty confident that they're going to do a great job."
Harding stopped all six shots he faced in relief for the Wild.
"I thought our execution was really, really good tonight," Yeo said. "I thought we were able to attack through the neutral zone with speed, I thought that our puck possession time was heavily in our favor, and obviously chances against, [Toronto's] a team that's going to get a few, and we limited them and we were able to generate a lot.
"So those are the things you have to do to win hockey games and we didn't get the result we deserved tonight. We've just got to bounce back."
Minnesota will continue its four-game road trip Thursday against the Tampa Bay Lightning. Toronto will face the Carolina Hurricanes at home Thursday.