Beaulieu and Mason Appleton each had a goal and an assist, and Connor Hellebuyck made 31 saves for the Jets (30-25-5), who are 5-2-1 in their past eight games and moved within one point of the Arizona Coyotes for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"Obviously it wasn't the prettiest goal I've ever scored, but it was a big one," Beaulieu said. "That game] was a grinder for us. We knew how important that win was for us, just the points in the standings. It wasn't our best game, but you've got to win those games at important, key times."
***[WATCH: [All Blackhawks vs. Jets highlights]*
Patrick Kane had a goal and an assist and Corey Crawford made 35 saves for the Blackhawks (26-25-8), who have one win in their past seven games (1-4-2) and finished 1-4-0 on their five-game road trip through Western Canada.
"I thought overall we played pretty hard," Blackhawks coach Jeremy Colliton said. "It was a pretty even game. Ultimately, I think the difference was they scored three goals on point shots, got traffic and gave themselves a chance to get a bounce. We had our chances to tie it up, but we need to find a way to generate some of those goals ourselves, especially in these types of games that are going to be this tight."
Beaulieu broke a tie when he one-timed Patrik Laine's feed from the right point. The puck redirected off Blackhawks forward Alex DeBrincat's stick and past Crawford to give Winnipeg a 3-2 lead.
"They collapsed so low that we had points open," Jets forward Blake Wheeler said. "On the first two goals, especially, we got some guys to the net and got some tips on it."
Ryan Carpenter gave Chicago a 1-0 lead at 15:44 of the first period, but Appleton tied it 1-1 at 6:38 of the second.