Anton Forsberg made 24 saves for the Sens (14-25-4) while Brady Tkachuk (2), Connor Brown and Evgenii Dadonov scored. Connor Hellebuyck turned away 20 shots as Kyle Connor and Nikolaj Ehlers had goals for Winnipeg (25-14-3).
"It was a fun game to get a win, finally, and for everyone to contribute," Sens head coach D.J. Smith said.
It took just five minutes for the Jets to take the lead as with Artem Zub in the box, Connor unleashed a one-timer from the left circle bar down for his 19th of the season.
Ehlers made it 2-0 with a low wrister from the right circle at 8:25 as he scored his 18th goal but the Sens got on the scoreboard on a power play goal of their own at 11:03 as Tkachuk got the faintest of touches on Josh Norris' shot for his 13th of the year.
The Sens completed the first period comeback as Brown scored for the eighth straight game at 18:38 as Hellebuyck got his glove on his shot from the slot but couldn't stop it from rolling in behind him as the teams entered the first intermission tied at 2-2.
"I thought all four lines contributed," Brown said. "Everyone played well … we played good games before that leading up against really good top-end teams that are ready to win cups now and we're making plays right with them.
"We're not hanging on by a thread or relying on our goalie. We're in the games and going play-for-play with them so there's a lot of positive things."
After a scoreless second, in which Winnipeg outshot Ottawa 14-7, Dadonov gave the Senators their first lead of the night with 9:50 to play as on Thomas Chabot's dump in, Hellebuyck misplayed the puck and the Russian swooped in to beat the reigning Vezina Trophy winner with a backhander for his 12th of the year.
Tkachuk added his second of the night with 3:48 to play as he beat Hellebuyck high over his left shoulder after coming in on a partial breakaway off the left wing to make it 4-2.
With his goal tonight, Brown became just the second player (Mike Green), and first forward, since 1999 to score in eight straight games as he extended his already set franchise record.
After being claimed off waivers earlier in the day from Montreal, defenceman Victor Mete made his Senators debut playing 9:43.
"It was definitely different," Mete said. No pre-game routine today. But I felt good and am very excited and happy to be here."
The Sens and Jets meet again Wednesday night.
