He did just that, too, scoring the lone goal in a shootout to give the Canadiens a 3-2 victory over the St. Louis Blues on Sunday night.
Kovalev beat Manny Legace with a high backhander on Montreal's third shootout attempt after the Blues missed on all three of their shots in the tiebreaker.
In the end, St. Louis might have lost more than just the game. Blues center Andy McDonald left the game late in the first period with what coach Andy Murray described as a fractured left leg and is out indefinitely.
McDonald went awkwardly into the corner boards in the Montreal end and was favoring his left leg and in obvious discomfort while being helped off the ice. He is set to undergo an MRI on Monday, according to TSN of Canada.
Kovalev followed Koivu and Andrei Kostitsyn in the shootout. Kostitsyn, who scored a goal and assisted on another in regulation, hit the crossbar with his attempt.
Kovalev went to the forehand, then pulled the puck back to his backhand and lifted the shot high over Legace.
"It was a pretty sweet deke," Montreal winger Christopher Higgins said. "I don't think anyone expects less from him right now because he's such a skilled player. "
Legace said he knew Kovalev was going there, too.
"I was just slow to react to it," Legace said. "He's a good player and can put it where he put it, probably two feet over my pad. Not too many guys can pull it that quick and bang, in the back of the net."
Robert Lang also scored in regulation for the Canadiens, who won for only the second time in six games after starting the season 8-1-1. Price stopped 24 shots.
The Canadiens were 0-for-10 on the power play and have scored twice in their last 36 chances. St. Louis was 1-for-9 with the man advantage.
Steve Regier scored twice for the Blues, and Legace also stopped 24 shots.
"We're talking about a team that most experts picked to win the Eastern Conference this year," Murray said, "and we lose in the shootout to them.
"I'm proud of the way our team battled here tonight."
Price gave the Canadiens a chance to win it with a pad save on Tkachuk's shootout attempt.
The Blues appeared on their way to a regulation victory until Lang tied it at 2 with 4:12 to play on an assist from Kostitsyn.
The Canadiens pounced on a Blues turnover, and Kostitsyn threaded a pass to Lang in the crease. Lang, whose initial shot was stopped by Legace, popped the rebound in out of the air.
"I thought tonight was one of our best games," Canadiens coach Guy Carbonneau said. "We were able to battle back in the third and win it in a shootout, so we're really happy."
Regier, recalled earlier in the day from Peoria of the AHL, took a feed from Perron in the low left slot and beat Price 3:24 into the final period to give the Blues a 2-1 lead.
The Blues' Cam Paddock won a faceoff to Cam Janssen, who collected the puck and snapped a shot from between the circles that deflected in off Regier in the crease past Price 3:48 into the opening period to give the Blues a 1-0 lead.
Kostitsyn's backhand that squirted through Legace's pads tied the game at 1 with 1:55 remaining after an outlet pass from Price.
Montreal D Mike Komisarek (strained shoulder) missed his second straight game after being injured during a fight Thursday night in Boston. ... Blues F Lee Stempniak has 10 points in his last six games after managing only one point in six games to begin the season. ... The assist for Price was his third career point. ... Montreal D Francis Bouillon took a shot to the mouth off in overtime and was immediately rushed off the ice.
Information from The Associated Press contributed to this report.