Tuukka Rask made 37 saves and stopped three of four attempts in the shootout for the Bruins (18-10-5), who have won three in a row. Rask is 7-0-1 in his past eight starts.
Torey Krug scored in the third period for Boston, which played without forwards Ryan Spooner and Riley Nash because of illness. Several Bruins were playing sick.
"I think for us in the locker room, when you win it's one more point, which it can come down to [at the end of the season], we've seen that around here. But it's the way you win," Boston coach Bruce Cassidy said. "We're missing guys down the middle of the ice. You've got guys battling through that weren't 100 percent playing today. So it always feels a little better when you can suck it up and get it done."
Hellebuyck made 32 saves, and Patrik Laine scored in the third period for the Jets (20-10-6), who had won two in a row.
"When you get into a game like that, your first reaction is to try to open it up or the stretch plays that didn't work in the game when we tried to run them," Winnipeg coach Paul Maurice said. "So we were pretty consistent with it. I think the effort was right, they competed real hard. ... We won't like what we gave up, we'll like what we got, and it was a slow bit of a grinder out there."
Bryan Little scored leading off the shootout, but Rask was able to keep Laine, Mark Scheifele and Nikolaj Ehlers from scoring. David Pastrnak tied it in the second round.
Krug gave the Bruins a 1-0 lead 8:16 into the third period. The defenseman intercepted a pass at the left point, skated to the top of the left circle and beat Hellebuyck with a wrist shot through a screen set by Noel Acciari.
Laine tied it 1-1 less than a minute later with a wrist shot from the bottom of the left circle at 9:13 after a slap pass by Ehlers.
"It was an unfortunate goal [by the Bruins]. He just shot it to the net and I don't know how it went in," Laine said. "Glad we found a way to bounce back."
