Tkachuk won with a one-timer from the right circle off a pass from Stutzle, who was sprung on a 2-on-1 by a stretch feed from Jake Sanderson.
“It's great play by [Sanderson] to read that we had a 2-on-1, and a great pass by 'Timmy,'” Tkachuk said. “It's been a grind to a certain extent, and yeah, I'm just really happy with the two points at the end of the day.”
Sanderson was the player who had forced overtime for the Senators, tying the game 2-2 at 18:06 of the third period with a point shot that deflected in off the stick of Jets forward Mark Scheifele.
“I mean, I think we lead the league in losses by one goal, and we made an emphasis at 6-on-5 that we weren't going to get denied," Tkachuk said. "So I mean, it took a little puck luck, but I think we're due for that.”
Nick Cousins also scored, and Linus Ullmark made 23 saves for the Senators (15-13-4), who concluded a three-game road trip 2-1-0.
“I really liked our third period,” Cousins said. “I thought it could have been easy just for us to mail it in with the way things have been going for us, but we dug in in the third, played a really good road third period, and got one with the goalie pulled. So, that was huge. ... Great road trip for us.”
Neal Pionk and Logan Stanley scored for the Jets (15-15-2), who have lost four of five (1-3-1) and 10 of their past 13 (3-8-2). Connor Hellebuyck made 28 saves.
“That is a game that should have been won by us,” Winnipeg coach Scott Arniel said. “At the end of the day, these are the games you've got to learn to win. ... We've got to find a way, however that is. If that's making the next play so that it gets out of the zone, if that's blocking a shot, whatever it is, those are the things [we need to do]. We need two points. We need them bad."
Cousins gave the Senators a 1-0 lead at 10:47 of the second period. Kurtis MacDermid sent a cross-ice pass to Cousins, who skated all alone down the right wing before scoring with a shot that went in off the blocker of Hellebuyck.