NEW YORK – The “Happy Birthday” song came flooding through the hallways of Madison Square Garden outside the visitors’ dressing room, because only after victory could the Washington Capitals so publicly acknowledge their youngest player’s 21st.

They had waxed the New York Rangers, 5-2, thanks to a furious forecheck during the second and third period, and multi-goal games from both forward Alex Ovechkin and forward Jason Chimera. They had beaten the Metropolitan Division leaders for the first time in three meetings, a necessary confidence boost with the playoffs around the bend. And now they blessed forward Tom Wilson, launching him and everyone else back toward the District with more revelry.

“They might be a potential first-round opponent, so you want to create some doubt in their mind,” Chimera said. “Obviously we did a good job coming into this building and winning. No better place to win. It’s a great atmosphere and a great place to play hockey.”

Even better when the Capitals delivered perhaps their most dominant period in a back-to-back all season, on the road with short rest after a failed comeback Saturday afternoon at Verizon Center. After Kevin Hayes and Derick Brassard scored within 61 seconds to close the opening period, whipping the home crowd into a frenzy and giving the Rangers a 2-1 lead, Washington punched back.

Ovechkin notched his league-leading 49th goal of the season, three seconds before a power play ended. The penalty kill snuffed Troy Brouwer’s tripping, Joel Ward’s slashing and Tom Wilson’s roughing, though the middle minor was aided by Brassard’s slash. Goaltender Braden Holtby made 23 saves after getting yanked against Nashville. Eleven players registered points, and four had two. After what Coach Barry Trotz called a “sloppy” first period, it was the comeback effort Washington needed.

“It was big,” Trotz said. “It was a big win.”

For Trotz to rejigger the lines in such a scrambled fashion, separating Ovechkin and Nicklas Backstrom for only the third game this season, at once showed a certain desperation with only seven games left in the regular season and a confidence in his players to figure matters out. Ward, the new top-line right winger beside Ovechkin and Evgeny Kuznetsov, tabled the first goal with a nifty pass off the boards. Brooks Laich and Eric Fehr aided Chimera’s goals with takeaways on hard forechecks. Even the fourth line, albeit scoreless, handled their counterparts well.

“I don’t know if you’re going to get a couple goals from each guy each night, but if we can get that through our lineup, then we have a chance,” Trotz said. “Ovi and Backie get a lot of attention. Ovi did his thing and he’s going to score, just because that’s what he does. But we’re going to need the secondary scoring to continue if you’re going to do anything in the regular season, and hopefully in the playoffs if we can get there.”

In the Eastern Conference, only the Rangers and Montreal Canadiens – now the only team Washington hasn’t beaten in either the Atlantic or Metropolitan Divisions this season – have clinched playoff berths, but victories like Saturday brought the Capitals much closer to returning. Ottawa, Boston, Pittsburgh and the Islanders, now all within six points of the Capitals, each dropped pucks while the team flew home, so a clearer picture would come later Saturday night.

Still, forward Troy Brouwer had insisted Washington needed confidence against the Rangers in particular. They found it here, then sang.

“The big positive tonight is how well we played in the second and third,” Holtby said. “We play that way, I don’t think there’s any team that can stay with us.”