Using a similar move to the one Koivu successfully completed to open the shootout, Kovalev deked Dwayne Roloson before tucking a forehand inside the left post.
"He did the same thing and it worked," Koivu said. "We've lost a few in the shootout and these are extra points that might be really big down the stretch. It's really big when you can come up with an extra point like that."
Roloson, who stopped 34 shots during the game, made a pad save against former teammate Sergei Samsonov before he was beaten by Kovalev.
"I thought I actually had him, but he was able to get it between the post and the bottom of my foot," Roloson said. "He made a good play. I tried to stay with him as best I could and he got his stick out just behind my foot."
"I felt I just had to make one save," Aebischer said.
"That was a great shot by Petr to tie it," Oilers coach Craig MacTavish said. "They're a good team. It was a hard-fought game and we had to pay a price to get the point."
Promoted to the Canadiens' top line because of leading scorer Christopher Higgins' ankle injury, Latendresse pushed the puck across the goal line behind Roloson 1:04 into the third for his first career point in his 14th game of the season.
"I was sure the puck was on the red line and I just tipped it," said Latendresse, who was credited with the goal after it was originally announced as Koivu's. "But if it was Saku who had scored, it would still have been the same thing, my first point."
Koivu was pleased with the rookie's effort in joining him and right wing Michael Ryder, who also assisted on Latendresse's goal.
"I thought he played really well," Koivu said. "He was probably nervous, the first game, getting a little more ice time, and obviously there are going to be things that we can read off each other with a little more time, but I thought he really played strong defensively and when you can create some offense and get the goal it's always a big plus."
Edmonton's Raffi Torres was called for tripping with 56.8 seconds remaining in regulation. Montreal's power-play opportunity was short-lived, though, because Mark Streit was also sent off for tripping just more than 4 seconds later.
Craig Rivet also scored for Montreal, which has won three of four.
Brad Winchester scored his first career regular-season goal for Edmonton, which has lost three straight and five of six.
"We played well tonight," Winchester said. "We wanted to get off to a better start. We haven't done that the last couple of games and we did that tonight and played a solid game. We were able to pull together and kill off some important penalties in the third, so we're happy to come away with a point and try to build off of that."
Higgins, who had eight goals -- including a league-leading three short-handed -- and 13 points in 12 games, will be sidelined for six weeks after injuring his ankle Saturday in the third period of the Canadiens' 2-1 loss to New Jersey.
He finished that game but was already held out of the lineup for the game against the Oilers when MRI results Tuesday revealed a partially torn ligament in his right ankle.
Winchester scored his first goal in 33 career regular-season games to put Edmonton up 1-0 at 13:54 of the first.
After Winchester and Canadiens defenseman Mike Komisarek squared off in the first of three fights in the second, Rivet scored his second of the season at 6:32, tying the game with a hard wrist shot to the top right corner off a pass from Streit.
- Winchester had one goal and two assists in 10 playoff games last season. He has four assists overall in regular-season play, including three in 14 games this season.
- Canadiens LW Sergei Samsonov got his 400th career point with an assist on Rivet's goal. Samsonov, who signed as a free agent with Montreal on July 12, had four goals and 11 assists in 19 playoff games last season with Edmonton, which acquired him in a trade with Boston on March 9.