Kevin Fiala had a goal and an assist, and Cam Talbot made 30 saves for the Wild (31-14-3), who have lost three of four.
"It's more frustrating how we started," Minnesota coach Dean Evason said. "I mean, full credit to Ottawa. They played hard and right and heavy and smart and aggressive, real aggressive. They took the game away from us early, and we couldn't catch up until the second period. … That team just continued to play the same way. We started wrong. They started right."
Chabot gave the Senators a 1-0 lead 2:09 into the first period with a snap shot that went under Talbot's right arm.
"It definitely gets you into the game right away when you score, and I think it was my second shift," Chabot said. "I skated a lot during the week, but there's nothing like actually playing a game."
Tkachuk made it 2-0 on the power play at 17:05 when he gathered the rebound of Chabot's shot off the boards and scored from a sharp angle at the right side of the net.
"That was some of the best hockey we've played in the first period," Tkachuk said. "We played heavy, we played aggressive, you know, getting on them. That's the type of game we want to play. Of course, we expected a pushback there in the second period from them. It was a fun game, an entertaining game, and we're just happy with the outcome."