Playing in his 27th game of an injury-riddled campaign, the defenseman fired a one-timer from the point that hit a Chicago player and got by goalie Corey Crawford to give the Jets a 3-2 lead. After the puck went in, Beaulieu pretended to throw a monkey off his back.
"Obviously it wasn't the prettiest goal I've ever scored, but it was a big one," said Beaulieu, who also had an assist.
Beaulieu missed time this season for three separate injuries, including broken bones in his hand and foot.
It was his first goal since Winnipeg acquired him from Buffalo at last year's trade deadline. His previous one came with the Sabres on Nov. 27, 2018. He has 12 career goals in 359 games.
Jets coach Paul Maurice was happy for Beaulieu and the third line's output.
"They play hard minutes, normally a lot of penalty-kill time and get some people to the net, but good for him, he's earned it," Maurice said.
Connor Hellebuyck made 31 saves for the Jets (30-25-5), who are 3-2-0 on a six-game homestand.
Crawford stopped 35 shots for Chicago (26-25-8), which completed a 1-4-0 road trip.
"No question disappointing not to have more points on the trip," coach Jeremy Colliton said. "Ultimately, we had three games that were acceptable and two that weren't good enough. We need more than that to get the points we need."
The Blackhawks led 1-0 after the first period.
Carpenter scored his third goal of the season after Kane sent a sharp-angled backhand pass to the front of the net and Carpenter redirected the puck past Hellebuyck at 15:44.
Jets forward Andrew Copp went in alone on Crawford about a minute later, but his shot missed the net.
Appleton tied it when he tipped in Beaulieu's point shot at 6:38 of the second.
Winnipeg appeared to go ahead at 9:05 on a goal by Kyle Connor, but it was reviewed and waved off because the puck went in off his arm. Roslovic gave the Jets a 2-1 lead at 15:37 when he tipped Kulikov's point shot.
"It's just a matter of getting pucks to the point and then getting bodies to the net and around the net," Appleton said. "Our first two goals were virtually the same exact picture. Third goal was another point shot."
Chicago tied it when Kane scored his 27th of the season with 53 seconds left in the period.
Beaulieu took a pass from Patrick Laine and fired the puck past Crawford at 1:36 of the third.
Kane called Beaulieu's winner an "unfortunate goal."
"I don't know how the guy got in the crease, but it looked like (Crawford) was a little bit tangled up and it kind of deflected off one of our guys and went in, so tough break," Kane said.
Players were unsure if the goal would be challenged.
"We didn't really know on the bench," Kane said. "We were kind of waiting to hear what the call was, so I guess they deemed it wasn't a good challenge."
Colliton said it was debatable.
"Yeah, of course (we considered it)," he explained. "We see there's contact but, you know, they've shown they're not going to overturn it unless it's pretty clear so that's why we didn't."
The Blackhawks tried to beat Hellebuyck in the final minutes with an extra man, but the Jets blocked shots and got their sticks on pucks to stymie those efforts.
No penalties were called in the game.
Blackhawks: Home against the New York Rangers on Wednesday.
Jets: Host the Los Angeles Kings on Tuesday.
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