Kovalev scored his 10th goal of the season and set up two by centre Tomas Plekanec as the Canadiens rebounded from their worst game of the season with a 5-2 victory over the Tampa Bay Lightning on Tuesday night.
"Actually, for the first time this season, (Kovalev) was telling us to keep it simple - and it worked," a grinning Plekanec said after scoring just his fourth and fifth goals of the season. "This was a good night and I hope it keeps going like that."
Michael Ryder also scored and Chris Higgins added an empty-net goal for the Canadiens (23-11-5), who were coming off a 3-1 loss in Tampa on Sunday night in which they were outshot 41-13.
Defencemen Doug Janik and Filip Kuba scored for Tampa Bay (18-20-2), which has lost three of its last four games.
The line of Kovalev, Plekanec and Sergei Samsonov has struggled for most of the season. Together, they have only 21 goals and they looked out of synch in many games while the top line of Ryder, Saku Koivu and Chris Higgins carried the offence.
But in this game, they were Montreal's best from their opening shift, firing seven shots overall at Johan Holmqvist and scoring their team's first three goals.
Coach Guy Carbonneau had been under heat from fans and some media to break up the line, and it is clear he has not always been pleased with their effort.
He said Kovalev "is one of the best players in the league when he wants to . . ." but tailed off before completing his thought. But he added that the threesome provided its own answer to whether they should stay together with their performance.
Kovalev used his size and soft hands to win battles and create space, Samsonov used his speed and Plekanec had a superb two-way game.
Kovalev repeated it came from keeping it simple.
"Sometimes we would try to control the puck, but it's all on the outside," he said. "This time, we created our chances. We always had someone in front. We did everything right."
The Bolts struck first when the Canadiens failed to clear a puck and Janik hammered it through traffic and behind Cristobal Huet at 9:18. It was the Agawan, Mass., native's first NHL regular-season goal in 50 career games, although he scored in the playoffs last spring.
Kovalev circled the net and fed Plekanec in the slot for a drive that trickled past Holmqvist to tie the game at 17:53.
Montreal outshot the Lightning 14-7 in the middle period, but the teams traded goals again.
Kovalev took Koivu's pass in the slot, deked past Ryan Craig and lodged the puck top corner, glove side on a power play at 15:44.
Only 31 seconds later, Martin St. Louis hit Kuba darting in from the point to tie it 2-2.
Kovalev battled for a puck behind the Lightning net and fed Plekanec, who saw his attempt to feed back to Kovalev bank in off the far post 6:01 into the third period.
At 13:52, Francis Bouillon's weak point shot was tipped by Ryder and flipped over Holmqvist and into the net. Higgins added his empty-netter with 19 seconds to play.
Koivu's two assists gave him 347 for his career to move past Pete Mahovlich for 14th place in Canadiens history and his 499th point gave him one more than Vincent Damphousse for 22nd place.
The Lightning began a four-game road trip that will take them to Minnesota on Thursday, Colorado on Friday and Pittsburgh on Monday.
"It's a key trip," Brad Richards said. "We're not in the playoffs as of Jan. 1, so we just have to look at that.
"We've been in a lot of games, but that's not good enough. I don't think we're far away, but we have to stop saying we're close and start winning games."
Montreal plays Thursday in Washington.
Notes - Bob Gainey, off since his daughter Laura was lost at sea on Dec. 8, has returned to work and attended the game. . . . The Bell Centre ice was marked with black spots from non-hockey events over the holidays. Kovalev said the ice felt like cement. . . . Defenceman Paul Ranger was scratched for a second straight game by the Lightning. . . . Defenceman Janne Niinimaa and forward Garth Murray weren't dressed for Montreal.