Clarke MacArthur and Erik Condra also scored for the Senators, who head home after earning seven of a possible eight points on their four-game road trip.
Despite controlling play and outshooting the Wild 15-3 in the first period, Ottawa led only 1-0 on MacArthur's 16th of the season.
With the Wild hanging around thanks to another strong effort from goalie Darcy Kuemper (29 saves), Condra won a race with Marco Scandella to a puck in front of the net and made it 2-0 at 5:55 of the third.
Turris scored on the power play at 17:38 of the third to put the game away.
Playing recently without forwards Mikko Koivu and Zach Parise and top goalie Josh Harding, the Wild had won five of their last six, scoring 21 goals during that span. But scoring opportunities were tough to come by against Ottawa, which is a much better defensive team on the road than at home.
When the Wild did get scoring chances, Lehner turned them away. Making his first start since losing 5-0 to Boston on Dec. 27, Lehner notched his first shutout since Feb. 28, 2012, against Boston.
Lehner's play picked up right where regular goalie Craig Anderson left off. Anderson is 6-0-2 over his last eight starts.
MacArthur's goal was his fifth in six games and happened after he redirected a centering pass from Turris into the net. Wild coach Mike Yeo wanted offside called on the play, and yelled at the officials from the bench as the teams lined up for the ensuing faceoff.
Kuemper was coming off his first career shutout on Sunday and has stopped 91 of 95 shots since being recalled from Iowa of the AHL on Jan. 2.
It was the second time Minnesota was shut out this season and the third time Ottawa has blanked an opponent.
NOTES: Harding took part in the morning skate, but there's no timetable yet for his return to game action. He missed his seventh straight game, and 11th out of 13, due to his recovery from an adjustment to his multiple sclerosis treatment. ... Parise skated on his own for the first time since before Christmas. He missed his 11th straight game because of a foot injury. "I can't predict what that means as far as when he'll be in the lineup, but an important first step for sure," Yeo said. ... Colin Greening became the 40th player in Ottawa history to skate in 200 games. ... Ottawa D Chris Phillips left midway through the third period after getting hit in the face with a puck.