Jordan Binnington, who made 24 saves in his first start in the Stanley Cup Playoffs, stopped Mark Scheifele with his right pad on a one-timer from the left circle with 13 seconds remaining.
"That buzzer couldn't have come sooner," Binnington said. "We were just battling throughout in our D-zone. It was a grind right until the end, so it was a good win."
Patrik Laine gave Winnipeg a 1-0 lead at 13:28 of the first period, taking a pass from Bryan Little in the high slot and beating Binnington glove side.
"We had a pretty solid game," Laine said. "We lost their guys in the third a couple of times and they got some good chances. They were able to score two, but overall, for two periods, we played some good hockey. It's a frustrating loss, but we've got to focus on Game 2."
David Perron tied it 1-1 at 4:05 of the third period when his shot from the right point made it through traffic before going under the arm of Jets goalie Connor Hellebuyck, who made 24 saves.
"We just kept climbing, climbing, grinding," Perron said. "Our second intermission, I thought we were calm and composed in here. It was good to see. Obviously, a lot of nerves to start the game. We put pucks deep, didn't make too many plays early on, but that's something we have to adjust and be confident to make those plays to allow us to have chances and score goals."
