Frederick Gaudreau scored, and Kaapo Kahkonen made 22 saves for the Wild (31-15-3), who have lost four of five.
"One mistake or one special player, right?" Minnesota coach Dean Evason said. "I don't think it was a mistake as opposed to him making a special play. He's one of the best players in the world for a reason. We really liked our game, certainly. They didn't have a shot for 10 minutes in the first period. We did a lot of really good things, and it was just a matter of one break somehow and they got it."
The Wild took a 1-0 lead at 8:37 of the second period when Gaudreau one-timed a pass from Matt Boldy, who was behind the net.
Matthews tied it 1-1 27 seconds later when he carried the puck through the neutral zone and shot from the top of the left circle.
"Our team is playing a good team game, but when not a lot is happening, you need somebody to make a play and be a gamebreaker," Keefe said. "That first goal he scored, there's a small number of players in the league that can score a goal like that, and the second goal, it was completely earned, completely effort-based.
"He finds a way to come through with huge goals at big times in the game, and he's done that all season, and you see the commitment defensively."
Matthews has scored 41 game-winning goals since entering the NHL in 2016-17, one behind Edmonton Oilers forward Connor McDavid for most since then.
"When it's 1-1 after (two periods) anyway, game on the road, it's a decent spot to be," Kahkonen said. "They obviously pushed and they have good players. But I think we had a good effort as well at the end there, but just didn't get a bounce tonight.
"Good players, him and Marner, but we've got good players too. What can you say? They're good players."