Parenteau redirected a shot by Milan Jurcina for his 12th goal and 50th point of the season at 1:36 of the third period.
Matt Moulson also scored for the Islanders (24-24-8) with his team-leading 25th goal of the season. Matt Martin sealed the victory with an empty-netter with 53 seconds left, assisted by Parenteau.
"We know we're not the best offensive team, but we know if we're patient and have enough skill from our top forwards that we're going to get it done," Parenteau said. "That's the main thing when we play on the road. I think we've been having success since we've been doing that."
The Jets opened the scoring when Thorburn scored his third goal of the season with 2:10 left in the first period off a rebound that went by Nabokov. Winnipeg outshot New York 16-10 in the opening period, but the Islanders came back early in the second.
Just 23 seconds after Jets forward Blake Wheeler went to the penalty box for tripping, Moulson scored at 3:55 of the second to tie the game at 1-all.
Moulson was playing in his 220th consecutive game with the Islanders. He hasn't missed a game since joining the club as a free agent in July 2009.
After Parenteau's goal, the Jets had a couple of power plays but couldn't beat Nabokov.
Jets coach Claude Noel is considering drastic changes to the power play to kickstart a crucial stretch of the season. In their past 10 games, the Jets have scored only two power-play goals in 24 chances -- and both came in a 3-2 shootout win over Washington on Feb. 9.
Winnipeg was 0 for 3 with the man advantage, and the Islanders connected on their only power play with Moulson's goal.
"I thought the power play really demoralized us again," Noel said. "It really seems to be the story of late."
Noel didn't accuse his players of not caring, just a lack of execution.
"It's got to the point where we have to make some drastic moves or change some things," Noel said. "You've got to either rejuggle, reshuffle the personnel, there's some things we have to look at.
"I don't know that it's necessarily personnel as much as decisions and stuff like that. That's the bothersome thing for me, is just that your best players aren't even executing passes that are simple plays."
Winnipeg is four points behind Toronto and the postseason cutoff in the NHL Eastern Conference.
"It's going to be a tough hill to climb," Noel said of the upcoming schedule. "To me, this is going to be the true test of what character we have."
The Islanders are 6-20-3 when allowing the first goal. ... The Jets travel to Minnesota for a game Thursday and then play eight straight at home.
Copyright by STATS LLC and The Associated Press
WINNIPEG, CANADA - FEBRUARY 14: Eric Fehr #17 and Mark Flood #36 of the Winnipeg Jets chat as they stretch in the...