Winnipeg had plenty of chances in the middle frame thanks to four power play opportunities and time after time, Lehner shut the door. His best save came on Mark Scheifele as he lunged out and denied the Jets centre with his blocker.
Scheifele would score the Jets first goal of the night on the team's 20th shot of the period. Nikolaj Ehlers one-timer from the top of the slot went off a stick and fluttered towards Lehner, Scheifele picked it up and back handed in his 23rd of the season.
In the third period, the Blackhawks would restore their two goal lead. Kirby Dach took the puck to the net and had his shot stopped, Hellebuyck failed to cover the rebound which allowed David Kampf to shovel it in for a 3-1 Blackhawk advantage.
At 14:14, Patrick Kane would become the 90th player in NHL history to record 1,000 career points when he got an assist on Brandon Saad's goal that made it 4-1.
Winnipeg scored with 2:09 left in the period with Hellebuyck on the bench in favour of the extra attacker. Laine put one behind Lehner to pull the Jets within two before Dominik Kubalik rounded out the scoring with a goal into the empty net.
"You can leave the road trip 2-1," said Maurice when asked about staying positive.
"You got to leave that door open for yourself. It's a challenge for us right now and you don't want that to build and become a bigger animal on the ice."
The trip continues in Raleigh on Tuesday when the Jets face the Carolina Hurricanes for the second and final time this season.