The Russian right wing scored with 24.3 seconds left in overtime to give Montreal a 4-3 win over the Buffalo Sabres on Saturday night.
Kovalev converted the Canadiens' second straight overtime power-play when he scored for the third game in a row following a 19-game drought.
"Since the start of the year he's the guy who has created the most scoring chances, but he seemed to be hitting a crossbar, or hitting a defenseman or something like that," coach Guy Carbonneau said. "We knew that once he got a goal he'd start to feel a little more relaxed, and that's what happened."
Kovalev, who led Montreal with 34 goals and 85 points last season, beat Ryan Miller with a wrist shot from the right side.
"Lately I've been more aggressive towards the net," Kovalev said. "Instead of looking for the pass or looking for the perfect play because sometimes it's definitely tough when you're not scoring as much and you kind of look for that perfect play because you almost want to score into an empty net. But sometimes you just have to let it go, get in a comfortable spot and let it go."
Sergei Kostitsyn scored his second goal of the game 15:06 into the third to draw Montreal even for the third time.
The Canadiens won their second in a row a losing three straight in regulation for the first time this season.
"We were battling all night long and it paid off in the end," said goalie Jaroslav Halak, who stopped 31 shots in his sixth straight start.
Kostitsyn, who also scored on a 5-on-3 power play in the second to tie it at 1, beat Miller from the left edge of the crease with 4:54 remaining.
Sekera scored a power-play goal 13:20 into the third that put the Sabres up 3-2. Buffalo took the lead for the third time when Sekera beat Halak with a wrist shot from the point through traffic and into the top right corner for his first of the season.
Alex Tanguay drew Montreal even at 2 earlier in the third with his 10th.
Miller made 42 saves after stopping 40 shots on Friday for his fourth shutout.
Referee Dave Jackson called his 1,000th NHL regular-season game. Jackson, who grew up in suburban Montreal, waved off a potential goal by Canadiens center Robert Lang 2:58 into overtime.
A video review showed that Lang knocked the net off its moorings before the puck crossed the goal line.
"For all the times you miss something, I had a pretty good view of this one," Jackson said. "I was in my hometown and Montreal scored in overtime, but you're paid to do a job, so I did my job and disallowed the goal."
Sabres coach Lindy Ruff had a problem with a pair of holding calls against his players, including Toni Lydman's minor early in the second that left Buffalo two men short and led to Kostitsyn's first goal, and Jochen Hecht's penalty 4:23 into overtime prior to Kovalev's winner.
"You're going to have to show me where Jochen is holding somebody," Ruff said. "Somebody is going to have to show me what Toni did to make it 5-on-3 ... because for the most part our discipline was pretty good. I can't find anything."
Roy extended his point streak to nine games when he opened the scoring with his 11th goal 9:10 in. The Sabres left wing drove the right side and cut toward the slot, where he put a wrist shot past defenseman Patrice Brisebois and beyond Halak.
Kostitsyn scored tied it at 1 with his second goal in two games at 5:17 of the second.
McArthur restored Buffalo's lead with his eighth goal at 15:21.
"You've got to give them credit, they kept coming. I thought our goalie played really well for us and it's just too bad we got into penalty trouble. They've got a great power play and they showed it."
- Jackson, honored in a pregame ceremony, is the seventh active referee to reach 1,000 games.
- Canadiens LW Andrei Kostitsyn missed the game because of a lower body injury. Kostitsyn appeared to injure a knee during Thursday's 5-2 win over Philadelphia. He is day-to-day.
- Montreal G Carey Price dressed for the first time in four games following a cold and a lower body injury. The Canadiens returned G Marc Denis to Hamilton of the AHL. Denis served as Halak's backup the previous three games and didn't make an appearance.