Ovechkin and Mike Knuble each scored twice as the Washington Capitals put a chokehold on their NHL Eastern Conference playoff series with a 6-3 victory on Wednesday night, despite being vastly outplayed for two periods.
Washington leads the best-of-seven series 3-1 and can end it with a win on home ice on Friday night.
The Canadiens, who lost a sixth straight playoff game on home ice over the last three seasons, face the prospect of a second straight early exit from the playoffs after being swept last spring by the Boston Bruins.
The big hero of the night was Varlamov, whose deft work with the catching glove led to a succession of brilliant saves as the desperate Canadiens outshot Washington 33-18 through two periods, including 21-9 in the second, only to emerge in a 2-2 tie.
"He was great," said Capitals coach Bruce Boudreau. "They had so many quality chances and if he's not at the top of his game, they're up 4-1.
"When you're outplayed like that and you go into the room tied, it's a relief because you know you only need to play 20 minutes of good hockey to win."
The Capitals outshot Montreal 20-6 in the third period and piled on four goals, although only two were on Carey Price, who had a decent if unspectacular game replacing Jaroslav Halak as Montreal's starter.
But for a second game in a row, it turned on a short-handed goal by the Caps.
This time, Roman Hamrlik knocked down Tom Poti's clearing attempt right onto the stick of Boyd Gordon, who went in on a two-on-one and feathered a perfect pass for Knuble to fire in with seven seconds left in the second period.
In Game 3 on Monday night, it was Gordon who scored shorthanded early in the second period to open the floodgates for a 5-1 Washington win.
A magic moment from Ovechkin put Washington ahead at 11:09 of the third and dealt a blow to Montreal's playoff hopes.
Defenceman Josh Gorges swept the puck off Alexander Semin's stick right to Ovechkin, who was breaking into the slot, and the Washington captain fired a low shot that gave Price no chance. Semin picked up his first point of the series on the play.
The Bell Centre crowd of 21,273, who had been in a roar through two periods, quieted noticeably as they sensed momentum turn to the visitors.
"I can't blame our effort, it was excellent," said Montreal coach Jacques Martin. "But if you make mistakes, they've got the skill and talent to capitalize.
"Ovechkin and Backstrom are elite players and if they get chances, they take advantage."
Only 52 seconds later, Matt Bradley fed Chimera for a goal with a pass across the crease and the rout was on.
Price was pulled with more than two minutes remaining and Knuble scored. Moore got it back, but Backstrom scored again into an empty net with 11 seconds to play.
After the Chimera and Backstrom goals, the frustrated Price was penalized for unsportsmanlike conduct, first for shooting a puck at a Washington player and then from the bench for contacting Backstrom as he skated by.
"He's an emotional person but he's still learning," said Martin. "You don't want to take away that passion, you just want to direct it the right way."
The first place overall Capitals, who scored 101 more goals than eighth-seeded Montreal in the regular season, have scored 19 times in four games and look to have broken the backs of the hard-working but probably overmatched Canadiens.
But Boudreau isn't counting Montreal out yet, pointing to their overtime win in Game 1 and a nervy 6-5 overtime win by Washington in Game 2 as evidence that the series is closer than it appears.
"I'd be frustrated if I was them," he said.
At least the Caps will head home having ended their run of futility on the power play. They went into the game 0-for-14 in the series and 0-for-21 dating to their last two regular season games.
On their second chance of the game, Ovechkin moved in on the left side and wired a shot inside the far post. The Caps power play, best in the NHL this season, is now 1-for-19.
Notes: Montreal defenceman Jaroslav Spacek, who had played especially well against Ovechkin, missed the game because he was sick. Martin said it was uncertain if he would be ready to return for Game 5. That brought Ryan O'Byrne into the lineup. Sergei Kostitsyn also played in place of Mathieu Darche. . . Washington defenceman Shaone Morrissonn also missed with an undisclosed injury and was replaced by Tyler Sloan. . . A scoreboard announcement appealed to fans to respect the U.S. anthem before the game and while a few tried to get a 'go Habs go' chant going, as they did before Game 3, by the end, all were quiet.