Kevin Hayes scored 3:38 into overtime for the Jets (46-29-4), who are two points ahead of the Nashville Predators and St. Louis Blues. Winnipeg, Nashville and St. Louis each has three games remaining, but the Jets have 44 regulation/overtime wins, three more than the Blues and four more than the Predators.
"They have elite players on that team, and when you get 3-on-3 (in OT), it's a lot of open ice," Hayes said. "We have some good guys on our team, and they have some fancy players on their team. It's fun, it's good for the fans. But ultimately, we got the two points, that's what we came here to do, and we're one step toward finishing in first place."
[WATCH: Jets vs. Blackhawks highlights]
Jack Roslovic had two goals, Adam Lowry scored, and Connor Hellebuyck made 25 saves for Winnipeg, which won for the first time in four games.
"Those are very important points," Lowry said. "We know just how tight the standings are, and to kind of get back on the right track going into [a game at the Minnesota Wild on Tuesday], to be able to answer … we gave up a late one again, but to answer in overtime, it was a heck of a goal by Kevin. Going into Minnesota, it's nice to kind of have that (losing) streak behind us. Hopefully, we can string some wins together."
Video: WPG@CHI: Lowry beats Crawford with short-side snipe
Dylan Strome had two goals, Jonathan Toews scored, and Corey Crawford made 35 saves for the Blackhawks (34-33-12), who trail the Colorado Avalanche by six points for the second wild card into the Stanley Cup Playoffs from the Western Conference. Each team has three games remaining.
"We wanted to drag it out as long as we could," Chicago coach Jeremy Colliton said. "There's still a chance, so we want to keep getting points, but certainly not satisfied with where we're at. We've made some progress, but we're all competitors, we want to go all the way."
Strome tied the game 3-3 with 2:20 remaining. The Blackhawks would have been eliminated with a regulation loss after the Avalanche earned one point in a 3-2 shootout loss earlier in the night.
"I think it was a huge goal to get it to overtime there," Chicago defenseman Duncan Keith said. "Obviously, we needed that, so somehow live to fight another day and worry about the next game and doing everything we can to just focus on that and try and win the game."
Toews gave the Blackhawks a 1-0 lead at 4:25 of the first period when his shot from the left face-off circle bounced off defenseman Jacob Trouba and between Hellebuyck's pads on the power play.
Toews set a new NHL career high for points in a season with the goal (77; 34 goals, 43 assists). He had 76 points (32 goals, 44 assists) in 2010-11.
Lowry tied it 1-1 at 10:49 with a wrist shot from the left circle.
Roslovic gave the Jets a 2-1 lead with 34 seconds left in the first after stealing the puck from Blackhawks defenseman Gustav Forsling and scoring with a sharp-angled shot from below the right circle.
Mark Scheifele was awarded a penalty shot 40 seconds into the second period after Toews was called for tripping him on a breakaway, but Crawford made the save.
Roslovic scored his second of the night with a wrist shot from the top of the left hash marks to make it 3-1 at 5:11 of the second period.
Strome got the Blackhawks to within 3-2 at 6:23 when he got to a loose puck with speed and scored from the slot.
Scheifele scored at 17:00 of the third period, but Colliton challenged for offside, and the goal was overturned after video review showed Blake Wheeler entered the zone ahead of the puck at 16:46.
"That's hockey, sometimes crazy things happen," Strome said. "I'm sitting there 4-2 thinking that our season is pretty much done because they're going up 4-2 with two minutes left, or three minutes left, whatever it was, then no goal, and then that happens. Obviously, take the positives."
Video: WPG@CHI: Roslovic steals and scores from sharp angle
They said it
"When you don't get the results, you can either feel sorry for yourself or keep playing the right way, keep doing the right things over and over again. We go on the road for these final four games, it's nice to win the first one and get a jump start there." -- Jets forward Kevin Hayes
Video: EA Sports Overtime Winner: Hayes seals it for Jets
"We're working hard every day and we're in every game. There hasn't been a game where we felt [terrible] about ourselves. We're right in every game and obviously we're still, I think, six points back, so I mean there's still some work to do, but just got to keep hope. Hopefully, good things happen." -- Blackhawks forward Dylan Strome
Need to know
Lowry has three goals in the past three games after he had nine in his first 72 this season. … Blackhawks forward Patrick Kane played his 900th NHL game. … Chicago forward Artem Anisimov played his 700th. … It was Strome's first multigoal game in the NHL.
Jets: At the Minnesota Wild on Tuesday (8 p.m. ET; FS-N+, TSN3, NHL.TV)
Blackhawks: Host the St. Louis Blues on Wednesday (8 p.m. ET; NBCSN, TVAS)
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