Gaudreau scored 32 seconds into the third period to cut it to 2-1, beating Saros short side from the bottom of the left circle.
"We're getting lots of pucks to the net," Minnesota coach Dean Evason said. "We got lots of opportunities. We're not scoring, obviously, but we're doing the right things to score. We just haven't found a way to put two, three, four together, but again, our power play has to generate and get us going in some areas."
The Wild went 0-for-5 on the power play, including a four-minute power play opportunity after Johansen was called for high-sticking Brandon Duhaime at 15:44 of the first period.
"I think it is a little bit of frustration," Minnesota forward Marcus Foligno said. "Those are power plays we've got to capitalize on those. Those are game-changers. Those win you games or make it close. There was a lot of movement out there and some good looks, but we need to cash in, especially when you get a four-minute power play. You've got to generate something more. If you don't get a goal, you've got to try to get momentum."
NOTES:Wild forwards Kirill Kaprizov (five points; two goals, three assists) and Mats Zuccarello (four points; one goal, three assists) each extended his point streak to four games … Duhaime had one hit in 7:13 of ice time after missing five games with an upper-body injury. … Duchene has 701 points (298 goals, 403 assists) in 921 NHL games … Nashville forward Yakov Trenin had one shot on goal, four hits and one blocked shot in 13:48 after missing one game with a lower-body injury.