Tyler Myers scored twice, Brandon Tanev had a goal and an assist, and Laurent Brossoit made 37 saves for the Jets (36-19-4), who have lost two in a row and five of their past seven games (2-3-2). Winnipeg is three points ahead of the Nashville Predators for first place in the Central Division.
"Always feels good to score, for sure," Myers said. "But it would have been nice to cap that one off. We had a tough one at home last game (4-1 loss to Colorado Avalanche on Thursday). To come back, tie the game in the third, it would have been nice to cap it off, get that extra point."
Myers scored his second of the game to tie it 3-3 at 14:01 of the third period on a one-timer from the high slot.
"It was a big goal by [Myers] to give us a point," Jets captain Blake Wheeler said. "Battled through a lot of penalties and found a way to get one."
Stone gave Ottawa a 1-0 lead on the power play at 1:38 of the first period, scoring on a one-timer from the left circle after Dmitry Kulikov took a double minor for high sticking.
Tanev scored on a shorthanded breakaway to tie it 1-1 at 2:56, pulling the puck to his backhand after deking Nilsson.
Myers scored another shorthanded goal for the Jets on a wrist shot at 5:33 to make it 2-1.
It's the sixth time in Jets/Atlanta Thrashers history they have scored multiple shorthanded goals in a game and the first time since relocating to Winnipeg in 2011-12. The two shorthanded goals in a span of 2:37 is the fastest in their history.
"You don't want to start a period like that, a game like that, but obviously, we weathered the storm," Brossoit said. "We scored more on their power plays than they did (in the first period). So you can take that as a good thing, it got us into the game."
Rudolfs Balcers redirected a point shot from Dzingel on the power play at 13:53 of the second period to tie it 2-2.
Ben Chiarot appeared to give the Jets a 3-2 lead at 14:08, but Boucher challenged for offside, and the call was reversed after a video review.
Duchene scored 47 seconds into the third period to give the Senators a 3-2 lead, converting a cross-crease pass from Bobby Ryan on the power play.
"To be able to be the better team for a full 60 minutes against a team like Winnipeg, it shows a really strong effort from us and a really good team game, so we definitely deserved the two points tonight," Nilsson said.
