Kirill Kaprizov scored his 20th goal of the season, and Marc-Andre Fleury made 39 saves for the Wild (20-13-2) who had won seven straight at home.
"Everybody in the world knows they're a shot-volume group and they tip," Minnesota coach Dean Evason said. "Their two most important goals are shooting and tipping. Conversely, we got pucks up to the top and we had lanes to shoot. We didn't. … It was a bit of a frustrating game in that aspect.
"But having said that, it was still a really good hockey game, really competitive hockey game. It was playoff atmosphere. It felt like it. Both teams were playing hard, playing well. They just caught a couple tips and got pucks to the net, and we didn't."
Seguin gave Dallas a 1-0 lead on the power play at 7:13 of the first period. Ryan Suter took a shot inside the blue line that was tipped wide by Radek Faksa, but Seguin scored on the rebound.
Kaprizov tied it 1-1 at 17:09 with a bank shot off Oettinger's back to extend his home point streak to 13 games (eight goals, 15 assists).
"I didn't know he was a threat from behind the net, but now I know that," Oettinger said. "Obviously, [that was] one probably I want back. I think there might be a bruise or something on the back of my head, but I'm happy we got the win."