Kane passed from behind the Winnipeg net to Ryan Carpenter in the bottom of the right face-off circle, and he sent the puck across the goalmouth to Brandon Saad for a tap-in that made it 4-1 Chicago at 14:14 of the third period.
"Great play all around, [Erik Gustafsson] to keep it in, Carpy making the heads-up pass to Saader backdoor to finish it," Kane said. "Nice to get it out of the way, nice to move on. As far as everyone coming onto the ice and sharing that with me is something I'll never forget."
[WATCH: All Jets vs. Blackhawks highlights]
Kane (31 years, 61 days) is the youngest United States-born player to reach the milestone, ahead of Jeremy Roenick (32 years, 13 days). The right wing has 380 goals and 620 assists in 953 games in 13 seasons, all with the Blackhawks.
Alex Nylander and Gustafsson each had a goal and an assist for Chicago (24-20-6), which won its season-high fifth straight game and is 11-4-0 in its past 15. Robin Lehner made 36 saves for his third straight win.
"Big win for us, obviously, and for Kaner to get his 1,000th point is a huge thing for our team and obviously for him," Blackhawks coach Jeremy Colliton said. "But I think everyone's pretty honored to have been a part of it. It was fun to watch and to get it on a night when we get two big points against a divisional opponent and in regulation, it feels good for everyone."
Video: WPG@CHI: Kampf taps in loose puck
Mark Scheifele and Patrik Laine scored for the Jets (25-20-4), who have lost four of five and are 4-7-2 in their past 13 games. Connor Hellebuyck made 28 saves.
"I think it's just generally talking about not being frustrated with our game here," Winnipeg defenseman Josh Morrisey said of their players-only meeting after the game. "We believe we're a good hockey team. We're in a fight to make the [Stanley Cup] Playoffs for a reason."
Nylander received a pass from Gustafsson and backhanded the puck past Hellebuyck's right pad for a 1-0 lead at 2:51 of the first period.
Gustafsson made it 2-0 at 14:11 when he faked a shot at the left point and skated up to the top of the circle for a wrist shot through traffic.
"Not a good first," Jets captain Blake Wheeler said. "They jumped on us, and I think as that period went on, we got stronger. Played pretty well the latter half … the latter 40 minutes of the game. Their goalie made some big saves. They jumped on their opportunities and jumped on a couple loose pucks, and that was the difference."
Video: WPG@CHI: Gustafsson nets wrist shot through traffic
Lehner made nine saves during a four-minute power play for the Jets after Drake Caggiula was called for interference and unsportsmanlike conduct at 4:20 of the second period.
"It's a good team over there," Lehner said. "Obviously, the first 10 minutes of the second was a bit of a workout, but we stuck with it, we battled hard together, and got through it."
Scheifele scored on his backhand from in front of the net to cut it to 2-1 at 18:17 of the second.
David Kampf tapped in the rebound of a Kirby Dach shot to give Chicago a 3-1 lead at 9:29 of the third.
Laine swept in the rebound of a Neal Pionk shot to make it 4-2 at 17:51, but Dominik Kubalik scored into an empty net at 18:26 for the 5-2 final.
It was Kubalik's 10th goal in eight games.
They said it
"I do like to see that. I think it's always more important, when you're struggling, that the players are coming together and not going separate ways, so it's good that they got together." -- Jets coach Paul Maurice on their players-only meeting
"Our habits are better and we're protecting each other with how we play. That's a big thing. And with that, you gain confidence. You gain confidence that the guy beside you is going to do the right thing, there's a little bit of peer pressure as well to do it for him. We're improving too." -- Blackhawks coach Jeremy Colliton
"It was unbelievable. I was kind of surprised at the time. There was five of us in the huddle, and then you kind of get pushed from behind and then we're all in the corner. The whole bench cleared. It's awesome, though. What a guy, what a player. I know we're all happy to have him, so it's big. Special moment for him." -- Blackhawks forward Brandon Saad on the celebration for Patrick Kane's 1,000th point
Need to know
Jets forward Adam Lowry left the game late in the first period after a hit by Caggiula, who received a minor penalty for interference. ... Kane is the 90th player to reach 1,000 points in NHL history and the 10th U.S.-born player. Three other players have had 1,000 points with the Blackhawks (Stan Mikita, 1,467; Bobby Hull, 1,153; and Denis Savard, 1,096). ... Kane has four goals and 11 assists during a 10-game point streak, the longest active streak in the NHL. ... Toews, who has four goals and nine assists during a six-game point streak, is one point from 800 in the NHL. ... The Blackhawks sent defenseman Dennis Gilbert and forward Brandon Hagel to Rockford of the American Hockey League after the game. Hagel did not play for Chicago after being recalled Thursday, and Gilbert has not played since Jan. 7.
Jets: At Carolina Hurricanes on Tuesday (7 p.m. ET; FS-CR, TSN3, NHL.TV)
Blackhawks: Host the Florida Panthers on Tuesday (8:30 p.m. ET; ESPN+, NBCSCH, FS-F, NHL.TV)
Video: Kane makes history in Blackhawks' fifth straight win