Mathieu Schneider and fellow defenseman Andrei Markov also scored power-play goals - set up by Kovalev - and Alex Tanguay and defenseman Mike Komisarek added even-strength tallies for the Canadiens, playing four of their final six on the road as they push for the playoffs.
The line of Tanguay-Koivu-Kovalev has scored 27 points in the five games it has been together and 12 of Montreal's past 21 goals.
Jaroslav Halak, subbing for No. 1 goalie Carey Price who came down with the flu Thursday, made 26 saves for his 17th win.
Montreal recorded 38 shots on Yann Danis and improved to 5-3-3 under coach Bob Gainey. The Canadiens are 4-0-1 in their last five.
Jeff Tambellini made it 4-1 in the second period for the injury-plagued Islanders, who were missing injured leading scorers Mark Streit (groin) and Kyle Okposo (groin) and played in front of a home crowd that largely supported the visiting Canadiens.
The chants of "Go Habs Go!" and "Ole! Ole! Ole! Ole!" filled Nassau Coliseum even before Koivu staked the Canadiens to a 1-0 lead with 6:57 left in the first, 34 seconds into rookie Sean Bentivoglio's holding penalty. Kovalev found Koivu with a pass in front for the captain's 16th goal.
Schneider, a former Islanders player, made it 2-0 with 1:29 left in the period when he ripped a shot from the center of the blue line - off a pass from Kovalev - that appeared to hit the stick of Islanders defenseman Radek Martinek before beating Danis. That came 7 seconds into Tim Jackman's cross-checking penalty.
That increased the cheers from the large pockets of red-clad fans throughout the arena.
Tanguay pushed the advantage to three goals 1:11 into the second with his 15th goal, and Markov made it 4-0 at 3:12 when he sneaked in toward the left post and finished a fine passing play started by Koivu and Kovalev. Markov needed only 30 seconds of Jackman's slashing penalty to score.
Tambellini beat Halak at 9:05 to cut the Islanders' deficit to three goals, but Long Island native Komisarek made it 5-1 just 44 seconds into the third period with his second of the season. Tom Kostopoulos had a chance to widen the lead, but he was stopped on a penalty shot by Danis with 15:56 left.
Notes: Montreal recalled G Marc Denis from Hamilton (AHL) to serve as Halak's backup. ... Kovalev has recorded multipoint games four times in five games (6 goals, 5 assists). ... Rookies C Trevor Smith and LW Sean Bentivoglio were recalled by New York from Bridgeport (AHL). Bentivoglio became the 13th Islanders player to make his NHL debut this season and the 16th rookie to play. ... Islanders C Andy Hilbert was knocked out of the game with a rib injury. ... New York has lost 542 man-games to injury.
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