Copp gave Winnipeg a 3-2 lead when he beat Corey Crawford up high from in close with 6:33 left after taking a perfect pass from forward Jack Roslovic.
''I just tried to make a quick move and go upstairs,'' Copp said. ''Great, great pass by Jack. That's a play where guys stay in the slot and look for that one-timer a lot, but (Erik) Gustafsson came out and really took that way, so I just saw some space behind him.
''And that pass was just fantastic, just to be on the same page as that. Great play by Rosie.''
Kyle Connor had a pair of goals, and Blake Wheeler and Patrick Laine also scored for the Jets, who trailed 2-0 after 20 minutes. Connor, with his team-leading 28th goal, and Laine added empty-net goals late to secure the two points.
Dominik Kubalik and Brandon Saad scored for the Blackhawks.
Connor Hellebuyck made 24 saves for the Jets, who won their third straight, while Crawford stopped 33 shots for Chicago.
Just 16 seconds after Blackhawks captain Jonathan Toews went off for hooking in the third, Wheeler took a pass from defenseman Neil Pionk and snapped the puck past Crawford to tie it at 2.
The Jets had pulled to within a goal at 2-1, scoring while shorthanded. With defenseman Sami Niku off for tripping, Copp pounced on a loose puck inside his own blue line, skated the length of the ice, then backhanded a saucer pass to Connor, who shot the puck on the bounce past Crawford.
''He makes a lot of really good plays, the little detailed plays that keep the puck moving in the right direction,'' Wheeler said of Copp. ''Offensively, he's getting more confidence with that puck and making some good plays.''
Crawford made several sparkling saves in the period, stopping Mark Scheifele in tight and Copp in alone on another short-handed effort.
Kubalik scored just 15 seconds into the game when he converted a pass from behind the net from Drake Caggiula.
The Blackhawks were all over the Jets for most of the period, making it 2-0 when Saad finished a perfect pass from Patrick Kane on Hellebuyck's doorstep. Hellebuyck, who stopped Toews on a breakaway, had no chance on either goal.
''We need to play all 60 minutes,'' Saad said. ''We know how big the game is. Just because we started off well, we obviously took our foot off the gas. They scored a nice short-handed goal and kind of took it to us the rest of the game.''
Toews recorded his 800th NHL career point, but was focused on the end result.
''That's a nice stepping-stone, nice to get a big number like that here in my hometown of Winnipeg, but unfortunately, we couldn't get the two points,'' Toews said. ''We were looking good the first shift of the game. I thought it was going to be one of those nights, but I think they bounced back and obviously played their best late in the game.''
NOTES: It was the second game of a six-game homestand for Winnipeg. ... The Jets are 14-12-3 at home this season. ... Winnipeg will induct Thomas Steen and Randy Carlyle into its Hall of Fame on Tuesday night.
Blackhawks: at Edmonton on Tuesday night.
Jets: host the New York Rangers on Tuesday night.
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