It was Ottawa’s third consecutive victory.
Connor Brown scored and added two assists, and Shane Pinto had two helpers for the Senators (22-27-5). Filip Gustavsson made 27 saves.
Mason Appleton and Mark Scheifele scored for the Jets (28-22-3), who have lost six in a row on home ice. Connor Hellebuyck stopped 19-of-22 shots in defeat.
Leading 2-1 in the third period, Stutzle restored Ottawa’s two-goal lead with his second goal of the night at 5:11 — a quick release up high from the faceoff circle past an off-balance Hellebuyck.
Stutzle nearly scored his third of the game late in the third but Hellebuyck robbed him with the glove. The rookie completed the hat trick with an empty-net goal with seven seconds remaining on the clock.
The Senators improved to 8-1-1 in their past 10 games.
The Jets were coming off a 4-0 playoff-clinching win over the Calgary Flames that snapped a seven-game losing skid and they carried that energy into Saturday’s contest.
Winnipeg buzzed around the net, cycled the puck with ease and tested Gustavsson early and often. They hit the post twice in a two-minute span.
But it was the Sens who broke the scoreless draw, against the run of play, when Brown deflected defenceman Victor Mete’s shot past Hellebuyck at 10:13 for his 20th goal of the season.
Before the Jets could regroup, the Senators doubled their lead 1:16 later through Stutzle’s deflection of Artem Zub’s shot from the blue line. The play was made possible by a bad giveaway by Hellebuyck behind his net.
Jets coach Paul Maurice’s men were leading 10-3 in shots but were down 2-0.
The first intermission did the Jets some good because they came out firing for the second.
Moments after a tremendous save by Gustavsson on Andrew Copp, the Jets wouldn’t be denied again as Appleton slashed the deficit at the 55-second mark. Scheifele stole the puck behind the net and fed Appleton in the slot for his first since Mar. 27.
Scheifele scored a consolation goal with 53 seconds left in the third period on a sensational saucer pass from captain Blake Wheeler before Stutzle completed his hat trick.
Winnipeg has three regular-season games remaining. The Jets host the Vancouver Canucks in a back-to-back set starting Monday.
Notes: Brown reached the 20-goal plateau for the second time after netting 20 for the Maple Leafs in 2016-17… Winnipeg defenceman Neal Pionk is day-to-day with an injury and did not skate… The Ottawa Senators are in Calgary on Sunday for their penultimate encounter of the season.
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