WASHINGTON - Thanks to sage, old Sergei Fedorov and a kid goalie with more career starts in the NHL postseason than the regular season, the Washington Capitals are headed to the second round of the playoffs for the first time in more than a decade.

And they didn’t even need a star turn from Alex Ovechkin to complete their monumental comeback.

Fedorov beat Henrik Lundqvist with 4:59 left in the third period, rookie Simeon Varlamov was good in the net when he had to be, and the second-seeded Capitals edged the No. 7 New York Rangers 2-1 in Game 7 of their Eastern Conference quarterfinal Tuesday night.

“Experience sometimes pays off. He knew what he had to do, when to do it,” Capitals coach Bruce Boudreau said about Fedorov. “That’s what makes him one of the greatest players ever.”

Washington is the 21st team in NHL history to win a series after trailing 3-1.

“Let’s face it: Realistically, we should have won the first six games,” Boudreau said.

It’s Washington’s first series victory since the 1997-98 season, when it reached the Stanley Cup finals. The success must feel particularly sweet to reigning league MVP Ovechkin and the 15 other players on the Capitals a year ago, when they also trailed 3-1 in the first round, and also forced a Game 7 at home — only to lose to Philadelphia in overtime.

Silent for stretches, even booing when the Capitals were tentative in the second period, the red-clad fans were loud as could be after Fedorov’s goal. Capitals players said their ears were ringing a half-hour afterward.

“They’ve really supported us and I really felt like we had to get a win for them tonight. We had to win,” Capitals general manager George McPhee said. “You can’t just have good seasons and not win in the playoffs.”

Still, the postgame celebration was kept to a minimum in the locker room.

“We have to try to keep our emotions,” Ovechkin said, “and get ready for the next round.”

Oh, and what a matchup that will be. The Capitals will host Sidney Crosby’s Pittsburgh Penguins on Saturday in Game 1 of a series pitting the past two NHL MVPs. Alex the Great vs. Sid the Kid.

Ovechkin had scored in three consecutive games to help Washington get its rally started, but he was mostly silent Tuesday, about 48 hours after proclaiming Lundqvist “can’t play every game like a god.”

New York’s Nik Antropov and Washington’s Alexander Semin traded first-period goals, and the Rangers were controlling a lot of the action thereafter.

“I felt so good going into that third period,” said Rangers coach John Tortorella, back on the bench after being suspended for squirting water on spectators and throwing a bottle into the stands in Game 5 at Washington.

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But it was Fedorov, playing in his eighth career Game 7, who determined the outcome. He took a pass from Matt Bradley and, with Rangers defenseman Wade Redden screening Lundqvist, sent a shot inside the far post for the winner.

“There was not much going on,” Fedorov said, “so I decided to shoot the puck.”

Good decision. The first player over to celebrate with the 39-year-old Fedorov, a past NHL MVP who won three Stanley Cups with Detroit? Ovechkin, who hopped on the back of his teammate and countryman.

The Rangers, meanwhile, registered only one official shot in the third period, making things easy in the late-going for Varlamov, who turned 21 on Monday.

Antropov put New York ahead about 5½ minutes into the game, but Semin tied it on a shot 10 minutes later that ricocheted off at least one Rangers player and fluttered past Lundqvist.

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There was plenty of gamesmanship and intrigue throughout the series: Ovechkin was ordered not to watch the Rangers practice before Game 3; Tortorella benched Avery for Game 5 for accumulating undisciplined penalties; Brandon Dubinsky accused Washington’s Shaone Morrisonn of biting him; and Boudreau risked going with Varlamov in place of 2002 league MVP Jose Theodore after a 4-3 loss in Game 1.

That last move looks brilliant now: Varlamov allowed seven goals in six games against New York.

“Like I always say: It’s nice to be young and not really know what’s going on around you,” Fedorov said.

Their season done, the Rangers will wonder how they let the series slip away.

“You look back and you say: We had ’em down, we had our foot on ’em, and we let ’em up,” Dubinsky said.

The Capitals now can look ahead.

“Short of winning the Cup, we’ve met every one of our goals: make the playoffs, win the division, get past the first round, sell out every game,” Capitals owner Ted Leonsis said. “We’re just checking them off.”

Notes: Capitals F Donald Brashear began serving his six-game suspension, mostly for a hit that broke a bone near Rangers F Blair Betts’ eye. “It’s like not having your big brother in the lineup to protect you,” Boudreau said. ... Capitals captain Chris Clark (wrist surgery) played for the first time since January. ... Betts was replaced by Artem Anisimov, brought up from the minors.

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