Kane was in on all of Chicago's goals on the night, setting up the first three tallies before adding an insurance marker late in the third to give the Blackhawks the win.
Kane took little credit for his performance saying his club played with a good measure of control.
"I think more than anything it's like it's easier to play hockey when you're playing with the lead and you focus on your defensive end or just being where you have to be on the ice and all of a sudden they're pressing to get offense and score, and that opens up more offense for us," said Kane. "Once we got the lead there and built on [it in] the 3rd, that's when more and more opportunities opened up for us."
Alex Nylander had a goal and an assist for Chicago.
Dominik Kubalik and Erik Gustafsson added singles for the Blackhawks, who moved to 14-16-6.
Robin Lehner stopped 36 shots for the Blackhawks Tucker Poolman scored the lone goal for Winnipeg.
Connor Hellebuyck made 28 saves for the Jets, who lost their second straight game and dropped to 20-13-2.
Alex Nylander got Chicago on the board early just under a minute into the opening period when he drove the net hard and converted a hard pass from Patrick Kane, who chased down a loose puck along the boards before hitting Nylander with a hard pass.
The Blackhawks winger took the feed in full flight, beating Connor Hellebuyck with a quick wrister just inside the right post.
The goal was his 5th of the season.
Chicago winger Brandon Saad was injured when he appeared to fall awkwardly on his right leg after being hit into the boards by Jet defenceman Lucas Sbisa at 11:41.
He left the game and did not return.
There was no scoring in the second period.
The Blackhawks were unable to muster much of an attack in the period, not registering their first shot on goal until there was 7:28 remaining.
Winnipeg outshot Chicago 14-3 in the second and 30-15 overall but still trailed 1-0.
The Jets had several chances to score but Lehner was equal to the task.
Dominik Kubliak scored 37 seconds into the third period when Patrick Kane saved a puck at the Winnipeg blue line before sliding the disc to Kubliak, who moved in and beat Hellebuyck with a low shot.
The goal was his 9th of the season.
Tucker Poolman got Winnipeg on the board at 5:09 of the third when he one timed a Nikolaj Ehlers feed from the corner past Robin Lehner, beating the Chicago netminder high glove side with a slapshot.
The goal was his 2nd of the season.
Chicago took a 3-1 lead with a power play goal at 10:58 of the third.
With Joona Luoto serving a too-many-men penalty, Erik Gustafsson one timed a Patrick Kane cross ice feed past Hellebuyck from the top of the right faceoff circle.
The goal was his 4th of the season.
Patrick Kane scored an insurance goal at 16:39, taking a cross ice feed from Alex Nylander at the blue line before moving in and wiring a wrister past Hellebuyck to make it 4-1 Chicago.
The goal was his 19th of the season.
Jets Captain Blake Wheeler said they failed to take their momentum away from the start and that hurt their game.
"It’s the opposite of what you think. The first period is the hardest in the second half of a back to back and then the second half of the game, you get better," he said. "When a team plays the night before and they come into your building, you got to take it from them the first half of the game, kind of how we did against Philly. The longer you let them hang around, the more they are going to build. We’ve done it to teams this year, too. The first period, certainly, and then as the game goes on, the ratio kind of evens out a little bit. Obviously, they were opportunistic tonight and it was deflating."
Chicago Head Coach Jeremy Colliton said he liked how his club handled the Jets, especially on the road.
"Obviously really happy with the start. I think probably the first 12, 13 minutes were excellent. They (Jets) got a little bit as the period went on. But even the second period they had a Little of the play, but I thought we did a good job defending. Bent but didn't break, got some big saves form Robin. And then how we played in the third period was really encouraging. We closed out a really good team on the road, so everyone should be pretty pleased with the effort overall," he said.
SHOTS-CHICAGO 32 WINNIPEG 37
NOTES-Chicago forward Brandon Saad will be out at least two weeks with an ankle injury. D Brent Seabrook didn't make the trip to Winnipeg and was dealing with a nagging injury.