Kovalev scored Montreal's second shootout goal after notching a goal and two assists as the Canadiens beat the Ottawa Senators 4-3 on Tuesday night.
"I know everybody's tired," Kovalev said. "We really put a great effort out there. It's not an easy team to beat and we'll take it in the shootout."
He scored his 300th goal in the third period and reached 700 career points with the first of his two assists in the second to lead Montreal back from a 3-0 deficit.
Kovalev scored the Canadiens' second shot against Dominik Hasek in the shootout, drawing his fourth roar of the evening from the sellout crowd of 21,273.
"The way the fans support me here is unbelievable," Kovalev said. "It gives you an extra boost and, I don't think I really need the confidence, but definitely gives you extra energy to come out the next time and beat the next team."
It was the first time the Canadiens had overcome a three-goal deficit to win since a 4-3 overtime victory against St. Louis on Dec. 10, 1997.
Pierre Dagenais scored on the Canadiens' first shot for his second game-winning shootout goal.
"I don't know who scored on the first penalty shot but I know Kovalev a little bit and I know he has everything, a good shot and he can deke," Hasek said. "Like I said before the season, during the season you win a few shootouts, you lose a few shootouts. Of course it's disappointing. There's nothing I can do. It's over, they scored a few goals."
"You have to respect who you're playing against, and we know that they're some of the best in the league right now," Huet said. "You approach it a little bit different when you face those guys, but you have to play your own game and what's working at the same time."
Kovalev, who missed 13 games because of knee surgery, set up second-period goals by Niklas Sundstrom and Michael Ryder to draw Montreal to within 3-2. The Bell Centre crowd erupted for the third time in just over 10:00 of play when he tied it with his milestone goal 4:13 into the third.
Hasek, making his first appearance against Montreal this season, made a sensational glove save on Ryder at 9:19 to keep it tied. He stopped 33 shots.
Ryder, the Canadiens' leader with 16 goals, has scored in five straight games.
Ottawa's Mike Fisher beat Huet, but his shot hit the left post squarely 2:46 into overtime.
"That was disappointing," Fisher said. "It was a nice play by (Heatley) to set it up."
Kovalev, who recorded his 700th point on Niklas Sundstrom's goal, had surgery on his right knee on Nov. 15 and had not played since he had a goal and an assist in a 5-4 overtime loss to Toronto three days prior to the procedure.
"It was really hard to get myself going in the beginning," Kovalev said. "The legs weren't there but I tried to push it through and my linemates helped me a little bit and it got easier in the second period. We started skating better and we stopped making mistakes in the defensive zone and started playing simple hockey."
The Canadiens are 13-3-3 with Kovalev in the lineup and 4-6-3 without him.
After the Senators built a 3-0 lead on power-play goals by defensemen Meszaros and Chara in the second, Montreal began its comeback with goals by Sundstrom and Ryder before the end of the period.
- Senators rookie Ray Emery won each of Ottawa's three previous games against the Canadiens. Emery has lost two straight since setting an NHL record with his ninth straight victory to begin his career.
- Kovalev recorded his 400th career assist in his last game against the Maple Leafs.
- Bonk missed his sixth straight game with a groin injury.