Kovalev had his 10th goal of the season as his line with Plekanec and Sergei Samonsov, which has struggled most of the season, was the best on the night for Montreal (23-11-5). Francis Bouillon also scored for the Canadiens and Chris Higgins added an empty-net goal with 19 seconds left to play.
Defencemen Doug Janik and Filip Kuba scored for Tampa Bay (18-20-2), which has lost three of its last four games.
The Lightning skated circles around Montreal in a 3-1 win in Tampa on Sunday night and did the same for much of the opening 20 minutes as the teams met again two nights later.
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 of the opening frame. It was the Agawan, Mass., native's first regular-season goal in 50 career NHL games, though he scored in the playoffs last spring.
Kovalev circled the net and fed Plekanec in the slot for a drive that trickled past Johan Holmqvist to tie the game at 17:53, helping Montreal escape the period tied 1-1.
A more hard-working Montreal team outshot the Lightning 14-7 in the middle period, but the teams traded goals again.
Kovalev took Saku 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 to bank a shot in off the far post 6:01 into the third period. It was only the fifth of the season for Plekanec.
At 13:52, Koivu fed Bouillon at the point for a weak shot that hit Holmqvist's stick and flipped over him into the net.
It was Kovalev's second three-point game of the season.
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. 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, but it didn't appear to affect the skaters. . . . 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.