The Wild finished with a split of their four-game road trip, which saw them play their past three games in four nights.
The game was a good bounce back for Kuemper, who gave up five goals on 32 shots in a loss to the New York Islanders in his previous start on Oct. 23.
"It's nice," Kuemper said. "Looking at the schedule going forward, it's going to pick up. We have a lot more games. It looks like I'm going to be getting more starts more regularly, so it's nice to get one like this under my belt so I can be confident next time my number is called."
Turris tied the game 1-1 at 5:06 of the third period.
The Senators had the first four power plays of the game, but their struggles with the man-advantage continued. They went 0-for-4 on Sunday and are 1-for-26 on the in the past 11 games.
"It's a big point," Senators coach Guy Boucher said. "Those points, they matter at the end. You make [the Stanley Cup Playoffs] or you don't, by one, two or three points. That point we got tonight is huge."