Paul Stastny had a goal and an assist and Mark Scheifele had a pair of assists for the Jets.
Dylan DeMelo, Blake Wheeler, Mathieu Perreault and Neal Pionk scored for Winnipeg.
Connor Hellebuyck turned aside 41 shots to pick up the win for Winnipeg, who moved to 8-4-1 on the season with 17 points, one back of the second place Montreal Canadiens and six back of the Scotia North division leading Toronto Maple Leafs who have 23.
Winnipeg has played two less games than Toronto.
Josh Norris scored the lone goal for the Senators.
Matt Murray made 21 saves for Ottawa, who started a five-game road trip with a loss.
There was no scoring in the first period.
The Senators outshot the Jets 18-6 in the opening frame, in a sloppy period of hockey for both clubs.
The tide turned early in the second period when Paul Stastny gave the Jets the lead eight seconds in, converting a Mason Appleton pass from the right corner after the Jet winger hustled to get to a loose puck following a dump in.
Stastny snapped the puck past Murray, beating him just inside the right post that was left exposed as he was moving across the net.
Dylan DeMelo made it 2-0 at 7:53 when he one timed a Kyle Connor feed from the corner past Murray which changed direction when it went off Evgenii Dadonov's stick before finding the net.
The goal was his first as a Winnipeg Jet.
Blake Wheeler scored Winnipeg's third goal on the power play late in the second period when he scored into an almost wide open net after Paul Stastny fed him a nifty cross slot pass.
The goal was his fourth of the season.
Marcus Hogberg replaced Murray at the beginning of the third period.
Mathieu Perreault scored 2:38 into the third, converting a Mark Scheifele feed, beating Hoegberg with a low shot to make it 4-0 Winnipeg.
Josh Norris scored 11:42 into the third, beating Hellebuyck in close after he spun around from close in before sliding hte Neal Pionk restored the four-goal cushion at 13:45 when he scored on a wraparound.
The goal was his first of the season.
SHOTS-OTTAWA 42 WINNIPEG 26