WATCH:All Jets vs. Blackhawks highlights
"That's the sign of a good team is responding to a little bit of adversity," Copp said. "They had a little bit of momentum in the third, and we came back and got that lead right back … and then killing off that four-minute power play at the end was huge."
The Blackhawks got the late power play after Jets defenseman Jacob Trouba was assessed a high-sticking double minor. Marian Hossa had the Blackhawks' best chance to tie it during the man-advantage, but Hellebuyck denied him at the right post with 2.6 seconds left.
Bryan Little also scored for the Jets (13-13-2), who won back-to-back road games after defeating the St. Louis Blues 3-2 in overtime Saturday.
Chicago played its sixth game without captain Jonathan Toews, who reportedly has a back injury. The Blackhawks played their second game without goalie Corey Crawford, who is out 2-3 weeks after having an appendectomy in Philadelphia on Saturday.
Scott Darling made 30 saves for the Blackhawks, who are 3-2-1 without Toews and have 12 goals without him. They haven't scored a power-play goal in the past five games (0-for-13) and have been outshot 254-238 in their past 10 games at 5-on-5.
"I still think we're playing the same style," Blackhawks right wing Patrick Kane said. "The onus is on offensive guys to try and produce and take control and create a little bit more out there. It's all across the board, but I think myself, personally, I want to do a little bit better as far as creating and getting chances. That stems from hard work and getting the puck back."
Winnipeg played its second straight game without Mark Scheifele, who was a late scratch against the Blues with a lower-body injury.