Ehlers scored off a Paul Stastny face-off win after Winnipeg rallied from down three goals in the third period.
"That's our team. I mean, we don't give up," Ehlers said. "We showed a battle at the end, and it paid off."
Connor Hellebuyck made 44 saves for the Jets, the No. 3 seed in the Scotia North Division, who can advance to the second round with a win in Game 4 of the best-of-7 series here Monday.
It was Ehlers' first game since April 24 because of an upper-body injury.
"You always dream of scoring these kinds of goals," said Ehlers, who had scored two goals in 25 Stanley Cup Playoff games entering Sunday. "But for me, tonight, it was a matter of getting out there, play simple and use my speed as much as possible. But you know, this was a team effort. A full, I don't know how many minutes we played, but a full 70-plus good effort. Great game and it's exciting."
Leon Draisaitl scored two goals and had an assist, and Connor McDavid had three assists for the Oilers, the No. 2 seed.
"We're in a good spot obviously, up 4-1," McDavid said. "They go on the power play, and we can't get a kill and kind of gave them a lifeline there, and they took advantage, obviously.
"We're not going to roll over and play dead on these guys. We've got to find a way to get a win tomorrow night and we'll take it from there."