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.
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.
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.
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.
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.
Pionk tied it 1-1 at 15:37 with a one-timer from above the circles that fluttered through traffic.
Stanley put the Jets in front 2-1 at 18:35, scoring short side under Ullmark's blocker with a wrist shot on a rush. It was Stanley's sixth goal in 32 games this season. He scored only five goals in his first five NHL seasons (202 games).
