MONTREAL (AP) -- With a three-goal lead after the first period, Cristobal Huet had plenty of time to contemplate whether he could keep Alexander Ovechkin and the Washington Capitals off the scoresheet the rest of the way.
Alexander Ovechkin hasn't slacked off after signing his record 13-year, $124 million contract on Jan. 10.
"Goalies say they don't think about it, but they do," Huet said after his 15th career shutout. "You can't change your mind, really. You've got to stay focused on the process to get there, not on the shutout itself. It's like winning a game. You can't focus on winning the game, you've got to focus on the process to get there."
Huet turned aside 15 shots in the first period and 13 in the second as Washington held small margins in shots in the opening two periods before being outshot 15-7 in the third.
"He just stopped everything," said Ovechkin, who had four shots overall.
Streit scored a power-play goal midway through the first and Kostitsyn finished off a two-man breakaway for a shorthanded goal at 16:53 that put the Canadiens up 2-0.
Koivu got his 10th goal at 18:25 to give Montreal a 3-0 lead to the delight of the sold-out crowd of 21,273.
"We had a really strong first period," Koivu said. "We wanted to get the fourth goal and we weren't sitting on the lead, but at the same time we were playing well defensively and playing smart defensively."
Kovalev eventually gave the Canadiens their fourth goal on a power play with 43 seconds remaining in the third after he took a Tom Poti slap shot off his right thumb early in the second.
"It's really blue," Kovalev said, holding up his bruised thumb, which had darkened under the nail with pooled blood. "I don't know if it's broken or not, I'm going to have X-rays, but it's just a thumb. I still have four fingers left."
Streit assisted on Kovalev's goal for his second power-play point of the game.
"As a five-man unit, they pass the puck better than anybody," Capitals coach Bruce Boudreau said.
Brent Johnson made 36 saves for Washington, which has lost two of three following a season-high four-game winning streak.
"I thought he played really well," Boudreau said. "I thought he was really sharp and solid and if it wasn't for him it would have been a worse score."
Streit opened the scoring 9:46 with his seventh goal after defenseman John Erskine was sent off when he cleared the puck over the glass for an automatic delay of game penalty.
Montreal had been killing a five-on-three for 32 seconds when Kostitsyn came out of the penalty box just as Canadiens center Tomas Plekanec broke down the ice.
Plekanec held the puck as he drove in on Johnson before passing left to Kostitsyn, who put a shot into the left side at 16:53 to make it 2-0.
Koivu increased the lead to three on an odd play moments later. The Canadiens' captain sent a pass the length of the ice and Johnson came out to play the puck before backing off as Montreal's Steve Begin hustled down the ice.
Begin fed the puck back to Koivu, who made it 3-0 with a shot from the slot.
Plekanec drew his second assist on Kovalev's goal. ... The Canadiens have outscored their opponents 16-5 over the course of their winning streak.