Ehlers scored at 2:20 of overtime, moments after Winnipeg goalie Laurent Brossoit made a nice stop against Drake Batherson.
''(Ehlers) can be so dangerous, such a dynamic player late in a game, just the speed to get into that hole and then make the play that finishes it,'' Jets coach Paul Maurice said. ''We need him to feel confident and healthy and strong, and when he is, he's just so very dynamic.''
Josh Morrissey tied it with 1:17 left in regulation with Brossoit on the bench for the extra attacker.
''It shows we don't give up,'' Ehlers said. ''We battled our (butts) off to stay in the game. ... It feels good to have the two points.''
Adam Lowry and Kyle Connor had the other goals for Winnipeg, which was outshot 41-28 in the contest. The Jets were coming off a 3-1 road loss to the Toronto Maple Leafs on Monday night.
''I guess you should wrap all of us up in our goaltending,'' Maurice said. ''That's the key in our game, our goaltending has been outstanding.''
Josh Norris, Chris Tierney and Alex Galchenyuk scored for Ottawa.
It's the first of three games in five days between the two clubs. They'll square off again in Ottawa on Thursday night before returning to Winnipeg on Saturday.
Winnipeg was without forward Patrik Laine (upper-body injury) for a second straight game. He was listed as day to day as the Jets opened a stretch with five games in seven nights.
Rookie forward Tim Stutzel, who's dealing with a nagging minor injury, didn't play for Ottawa. The third overall selection in the 2020 NHL draft, who has a goal through two games with the Senators, is also considered day to day.
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