The 34-year-old right-winger scored two goals in each of the Canadiens last two games - a 4-1 win over Washington on Saturday and a rousing 6-4 victory over the New York Rangers on Tuesday night. Kovalev, who is paid US$4.5 million per season to be one of Montreal's big guns on attack, had scored only 14 goals in his first 65 games this season.
"I'm not doing anything extra, I'm just playing my game," he said Wednesday. "I just want to take this team to the playoffs.
"There's nothing better than playing in the playoffs. We could have been resting and getting ready for the playoffs now, but we put ourselves in this position and have to recover from that."
The win over New York was the Canadiens' fifth in a row and put them back into playoff position in the NHL Eastern Conference, but the race changes daily with six clubs battling for three spots.
Montreal, which has five games left, next plays in Ottawa on Friday night and at home Saturday night against the first-place Buffalo Sabres.
Critics will say the Canadiens could have had a playoff spot cinched had Kovalev played all season with the intensity he has shown recently.
As it is, he won't come close to the 65 points he put up in 69 games last season, not to mention the 95 points, including 44 goals, he got for free-wheeling Pittsburgh in 2000-01.
But he has saved his best hockey for the end of the season and the playoffs in the past, and his teammates are glad to see him battling again.
"When the chips are down, he's got a sparkle in his eye," said defenceman Mathieu Dandenault. "He wants to carry this team to the playoffs.
"He's driving to the net and scoring some ugly goals that he's paying the price for. And he's certainly helping the team win."
His recent goals have all come from going to the net and using his six-foot-one 225-pound frame to get pucks in from the edge of the crease.
Kovalev's right eye was still swollen and stitched Wednesday from a clip by Matt Cullen's stick on a power-play goal that ignited a five-goal second period against the Rangers.
"I went to the net and I got hit right before the shot, but I knew where the puck was so I went down and waited for the crowd reaction," he said.
"When the whole team plays well, you look good. People ask me why I didn't score at the beginning of the season, but the other guys were scoring. Now, other guys aren't scoring and I am, so it works good for the team."
If it were only that simple.
In fact, he's had a mostly awful season. Early on, his line with Sergei Samsonov and Tomas Plekanec was a disaster and when top-line winger Chris Higgins was injured, the Canadiens laboured for goals.
Many line juggles later, Samsonov looks to be a permanent scratch, not dressed for eight games and counting, while Kovalev has found new life playing with rookies Maxim Lapierre and Guillaume Latendresse.
And with new linemates, Plekanec has been Montreal's best forward in the second half of the season, with 17 goals and 18 assists in 38 games since Jan. 2.
Along the way, Kovalev was blasted publicly by Canadiens legend Guy Lafleur for being selfish and pulled himself out of the lineup in the midst of a February slump for seven games with a sore elbow.
He was also in the spotlight for a Russian radio interview in which he allegedly said coach Guy Carbonneau doesn't like Russian players and that francophone players had split the team into cliques. He has denied ever making the comments.
And he recently missed two games with a nasty case of vertigo.
All seems to be forgiven when he plays like the star general manager Bob Gainey felt he could be when he signed him to a four-year contract in 2005.
Dandenault compared Kovalev to Sergei Fedorov, a former teammate on three Stanley Cup champion teams in Detroit who was not always at his best in the regular season, but shone in the post-season.
"That's the mentality of a talented player - you want him there all the games and to score two every game, but it doesn't work that way for everyone," Dandenault said. "(Kovalev) had some injuries, but we saw in the playoffs last year that he can really dominate a series. Now he sees that we're so close to being in or out and he's leading the way. That's what we need."
Kovalev called it a frustrating season in which, until recently, little that he tried worked. When he went to the net, the puck wasn't there. When he went to the slot, the puck went to the net.
Now, he goes to the net a lot. And lately he's shown more and more trust in Latendresse and Lapierre, chipping pucks into the zone for them to chase instead of trying to carry the puck across the blue-line.
Montreal acquired Kovalev from the Rangers late in the 2003-04 season and he helped them reach the second round of playoffs. Last season, he had seven points in six playoff games as the Canadiens lost to Carolina in the first round.
In the post-season, he has averaged a point per game for Montreal.
He said that motivates him to get into the playoff again.
"It's just more exciting," he said. "Everyone's waiting to see what happens next."