It was Oettinger's second career shutout in the Stanley Cup Playoffs and the first by any NHL goalie this postseason.
"Oettinger]'s just dialed in right now," Stars forward Jason Robertson said. "That's obviously important in the playoffs. We want to limit more of the chances we give to him, but we know we have one of the best goalies in the world behind us. Definitely an advantage."
Dallas leads the best-of-7 series, 3-2. Game 6 is in Minnesota on Friday.
[RELATED: [Complete Stars vs. Wild series coverage]
Roope Hintz had three assists, and Tyler Seguin and Robertson each had a goal and an assist for the Stars, the No. 2 seed in the Central Division. Hintz has six points in his past two games after he had three assists in Game 4 on Sunday.
"I think we're getting better as the series goes on," Dallas coach Peter DeBoer said. "We got behind early, we've chased it. We wanted to take the opportunity to get out in front for the first time in the series. The last win is always the toughest, but we've got an elimination game in Minnesota. We've been a real good road team all year. I think our guys are excited."
Filip Gustavsson made 21 saves for the Wild, the No. 3 seed in the Central.
"Well, hopefully we can use these next couple of days to recharge and rejuvenate, get excited," Minnesota coach Dean Evason said. "We didn't have our best stuff obviously tonight for whatever reason. So yeah, two days, we expect our group to be excited, jacked to get home. Win one game and see what happens in seven."