Jets goaltender Connor Hellebuyck stopped a shoot in and left the puck for his defenceman, who never arrived.
Instead a hustling Connor Brown picked up the disc and fed Mike Reilly at the left point who got a shot on goal which Tkachuk got his stick on and beat a surprised Hellebuyck blocker side to give the Senators their third win of the season.
Ottawa hung around all afternoon, getting in passing lanes and were aggressive along the boards, making it difficult for a more skilled Jets squad time to set up.
Evgenii Dadonov scored the other Ottawa goal on the afternoon, a second period tally.
Filip Gustavsson stopped 30 shots for the Senators, who now sport a 3-12-1 record.
Connor Hellebuyck made 27 saves for the Jets, who dropped to 8-5-1.
There was no scoring in the first period.
The two clubs exchanged goals 1:46 apart in the second period.
Winnipeg's goal came 5:43 into the second when Mark Scheifele backhanded a Kristian Vesalainen pass from the left side boards past Ottawa goaltender Filip Gustavsson to put the Jets ahead 1-0.
The goal was his sixth of the season.
Ottawa followed suit at 7:29 when Evgenii Dadonov redirected a puck off a nifty pass from Colin White past Connor Hellebuyck to make it 1-1.
White took a feed from Nick Paul, who stopped the puck from exiting the zone before moving across the slot and sliding the disc between a sprawling Neal Pionk's legs.
Dadonov put his stick down in time to deflect it past Hellebuyck to get Ottawa on the board.
SHOTS-OTTAWA 29 WINNIPEG 31