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."
