Montreal, which outshot Winnipeg 44-24, is 5-1-1 in its past seven games.
"We've talked about this the whole time," Canadiens defenseman Shea Weber said. "We're not giving up. We're not out yet. Six more points available for us. We'll take the next game here and try to win that one and see what happens."
Joel Armia converted a tic-tac-toe play on the power play at 17:05 of the first period to give Montreal a 1-0 lead.
"I think we just need to keep playing like that every game," Armia said. "Every game is big right now. Today we just kept it simple and played really fast I think through the whole 60, so that was the key."
Jeff Petry's point shot found its way through a crowd in front of Hellebuyck to make it 2-0 at 19:23 of the second period.
"We just need to dig a little deeper here," Hellebuyck said. "We're right in it. Real close. Going to continue grinding, wear teams away and get that extra one or that extra block or that extra stop that's going to win us these games."
Matthieu Perreault pulled the Jets to 2-1 at 11:24 of the third period, but Weal made it 3-1 into an empty net at 19:44.
"They're a desperate team and that was a playoff-type of game," Wheeler said. "We're going to have to get used to playing that type of game."