Peters finished with 27 saves, including a breakaway stop on Byfuglien in the second when Winnipeg was ahead 1-0.
It was Postma, though, who beat Peters with a high shot over his glove with three seconds left on a power play to make it 2-0 at 8:27 of the period.
Ruutu scored with a shot that rang off the inside of the post on Pavelec's stick side and zipped across and into the netting at 10:38 to make it 2-1 heading into the third.
Hurricanes coach Kirk Muller, coaching in his 100th NHL game, wasn't surprised his team fought back from a 3-1 deficit midway through the final period.
"That's the way our guys have been playing," he said. "We haven't got the breaks or the results that we, to be honest, we really deserve in our performance in the last three, four weeks. So it's unfortunate because I'm really proud of the guys the way they've been battling, playing hard and playing well.
"When it does change, they're going to get rewarded and it will pay off somewhere along the line."
Notes: Ladd extended his points streak to six games, tying a career high. He has four goals and eight assists in the streak. ... Jets C Bryan Little played his 400th NHL game and had one assist to stretch his points streak to five games (one goal, eight assists). ... Wheeler is also on a five-game points run with three goals and seven assists. ... Staal has six assists in his last six games.