Montreal seeks a fifth straight victory as it hosts Nashville on Saturday night.
The Canadiens (5-2-0) have scored first in their last three games and jumped out to a three-goal lead in each of their last two. They blew that advantage Thursday against Columbus, though, before Tomas Plekanec scored with 1:07 remaining and added an empty-net goal for a 5-3 win.
Montreal scored twice in the first 11:28 in Tuesday's 3-0 win over Winnipeg, but it didn't score again until Danny Briere's empty-netter with 1:18 to play.
"We said that we can't take our foot off the gas. We did it in Winnipeg and got away with it," reigning Norris Trophy winner P.K. Subban, who had two assists Thursday to extend his point streak to six games, told the team's official website. "On Thursday night, it almost nipped us in the bud. We've got to play a full 60 minutes here. We can't always rely on our goaltender to shut the door."
Carey Price made 30 saves and is 4-2-0 with a 2.01 goals-against average.
"We really just kind of gutted the (last few) wins out. There's no real secret to that," Price said. "I think most teams that win give their best every night, and if we don't have our best performance, at least we're going to give our best effort."
Nashville (3-3-1) has scored first in each of its last three games, but it got only Matt Cullen's first-period goal before missing all three shootout attempts in Thursday's 2-1 loss to Los Angeles.
The Predators, who had won two straight, have put at least 30 shots on net in four consecutive games.
"We're getting good chances, so if we continue to do that we're going to be fine," said Craig Smith, who has a goal and three assists in his last three contests. "You want to say it's just dumb luck that the pucks are just bouncing off of our sticks, but if we continue to do the right thing, things are going to happen."
Cullen scored his first goal since signing a two-year, $7 million contract as a free agent this offseason.
"I think we have some guys with some good speed and creativity that are making some things happen," Cullen said. "We just have to continue to improve and work on our game and move ahead."
Pekka Rinne has struggled at times, posting a 2.73 GAA and .901 save percentage, but he made 29 saves Thursday in a solid performance. He's 2-1-1 with a 1.25 GAA in four career starts against the Canadiens, who played their last contest without forward Max Pacioretty after he suffered a strained left hamstring against Winnipeg.
Pacioretty is expected to miss three weeks.
"It's bad luck, but it could have been a lot worse," coach Michel Therrien said. "We'll take time to make sure he gets better, but it the meantime, it's not such bad news. It could have been worse."
Price has lost both of his starts against Nashville with a 2.50 GAA. He wasn't in net the last time the teams met Nov. 12, 2011, when Pacioretty scored in overtime to give Montreal a 2-1 victory.