Vatrano tied it 2-2 on a power play at 5:40 of the third with a one-timer from just inside the blue line.
"We're a resilient type, no matter what we face," Connor said. "We have the confidence in here, in each other, that we'll get out of it, it's going to make us stronger. Especially coming down to the playoffs, you're not going to win every game, so you've got to deal with those situations when they happen."
Dostal, who made his third start this month, made a save on Connor's breakaway at 7:50 of the first, and used his right pad to kick aside a backhand from in close by Morgan Barron at 10:02.
"He's just dipping his toe in the water here," Ducks coach Dallas Eakins said of Dostal. "It's important that we really try to get him as many reps as we can, and that's what we're going to try to do down the stretch here."
NOTES: Winnipeg has won five in a row and is 13-2-1 in its past 16 games against Anaheim. ... The Jets went 0-for-2 on the power play and are 0-for-21 in their past six games, the first time they have gone six consecutive games without a power-play goal since Oct. 28-Nov. 6, 2016.