Connor Hellebuyck made 28 saves for the Jets, the No. 3 seed. Adam Lowry scored in the second period to end Winnipeg's goal drought at 99:31.
"It's nice to get one behind [Price]," Lowry said. "Earlier in the year, I think everybody was ready to run Carey out of town and he couldn't find his game. Now he's back to the form that they all expect. It's in our best interest to chip away at that confidence and you just continue to get bodies to the net. He's a world-class goalie for a reason."
Montreal has not trailed for 376:14, dating to the start of Game 5 against the Toronto Maple Leafs in the Stanley Cup First Round, the fifth-longest streak in NHL playoff history. But Canadiens forward Brendan Gallagher said he is mindful of when they fell behind 3-1 to the Maple Leafs before coming back to win the series.
"We know we're in a nice little rhythm right now, but we went through this last series and we know how quickly these things can change," Gallagher said. "We obviously have the advantage right now, but you've got to make sure that you don't give the other team any life, any hope."
Game 4 is here Monday (8 p.m. ET; NHLN, NBCSN, CBC, SN, TVAS).
"I think it's great for us right now, to be honest with you," Jets captain Blake Wheeler said. "Having to sit in a hotel room all day tomorrow and stew on that one, you would have a lot of guys burning inside. … Hopefully we get a good feeling in our room and start to rebuild ourselves. We've got to win a hockey game, no different than it was today. We've got to win one game, and then we'll see what happens."
The Canadiens have not swept a best-of-7 series since 2014 against the Tampa Bay Lightning in the Eastern Conference First Round.
"We know how difficult this is going to be," Gallagher said. "It's always difficult to put a team away. We were obviously on the other side of it last series. As soon as you get a sliver of hope, the momentum starts to build."