Brodeur got his 615th career win despite leaving after the first period because of a bruised right leg. Brodeur stopped all 11 shots he faced before he was replaced for the second by Johan Hedberg, who made 14 saves over the final two periods.
"I went into a butterfly and my leg got caught up under me and I kind of heard a click," said Brodeur, who watched the third period in Devils GM Lou Lamoriello's box. "[Monday] we'll see how it feels. I don't think it's anything major."
Kovalchuk was awarded his second goal of the game at 18:39 of the third when he was hooked on a shot at an empty net that hit the right post. Travis Zajac, who scored in the second, got his second assist of the game on the play.
"I knew it was going to be a goal because it happened to one of my teammates, [Marian] Hossa, in Atlanta," Kovalchuk said.
P.K. Subban got his sixth goal 6:32 into the second, moments after Zajac made it 3-0, to spoil the combined shutout effort.
Carey Price made 26 saves for Montreal, which had won three straight coming out of the All-Star break, including a 2-0 win over the New York Rangers on Saturday.
Zubrus opened the scoring on an unassisted effort 1:12 in. The former Canadiens forward jumped on a turnover by Montreal defenseman Hal Gill behind the net and came out front to beat Price for his 10th goal.
"He was trying to bank it to me," said Subban, Gill's defensive partner. "We've done those plays a million times and they get there and I take it and we go up the ice and break out of our zone easy."
Kovalchuk deflected Colin White's point shot in midair, redirecting it past Price for his 16th goal at 4:04.
Brodeur flexed his right leg at the Devils' bench during a stoppage in play with 5:45 left in the opening period moments after stopping a shot by Jaroslav Spacek. He finished the period but did not return for the second.
"I saw Marty being in discomfort so I had a little time to prepare," Hedberg said.
Zajac made it a three-goal lead with his ninth goal 3:16 into the middle period.
Subban drew Montreal within 3-1 when he was credited with his sixth after his shot struck Kovalchuk's stick on its way past Hedberg at 6:32.
"It was just one of those games where the puck just didn't bounce our way in the first five minutes, but that's hockey," Subban said. "You've got to stick with it and battle through it and I thought we did a pretty good job."
- Brodeur, a Montreal native, improved to 40-16-5 overall against the Canadiens.
- Montreal D James Wisniewski missed his second straight game because of illness.