WASHINGTON — By virtue of the quirky way the NHL decides tie games — with a skills competition that rewards the team that loses — the Islanders and Capitals have completed a steady climb into playoff position.

The Capitals won a shootout to beat the Islanders 2-1 Thursday night, moving Washington atop the Southeast Division and the Islanders into seventh place in the Eastern Conference.

Braden Holtby made 35 saves and then was perfect in the shootout, and Washington also got the help it needed when the Canadiens finished off a 4-1 win over Winnipeg. The Capitals and Jets both have 38 points, but Washington has two games in hand.

Meanwhile, the Islanders picked up a standings point and benefited from the Devils’ 1-0 loss to the Bruins. In the metropolitan area’s three-way race that takes up the middle of the standings, the Islanders have won five of seven games and stand at 40 points, and the Devils and Rangers each have 39.

The Islanders are trying to make the playoffs for first time since 2007, which also happens to be the last time the Capitals weren’t in the postseason.

“We’ll take the point,” Islanders coach Jack Capuano said. “It’s on the road, tough building to play in against a real good hockey team. So, yeah, we’d like to get the two, but one is better than none.”

The Capitals also have momentum, winning six of their last eight, no longer resembling the team that started 2-8-1 in the lockout-shortened season.

“It’s been a tough season in that aspect — always looking up,” Holtby said. “We all knew we’re capable of [being] where we should be, and that’s at the top. You know, this last little while we’ve all focused on what we need to do, and that’s be successful. And we knew if we do that, we’ll be where we want to be at the end of the year.”

Mike Green scored on a wrister from the right circle with 13 seconds remaining in the first period for the Capitals, and Alex Ovechkin was the only player from either team to find the net in the shootout. Green has five goals in his last four games.

Holtby was stellar, with fans chanting his name when he denied Frans Nielsen and John Tavares in the shootout and got a break when Brad Boyes lost control of the puck while skating in on net. Making his 10th consecutive start, Holtby needed seemingly every reflex he had, whether it was sliding left to blunt Keith Aucoin’s attempted tap-in at the edge of the crease in the first period or sticking out his right pad to thwart Andrew MacDonald’s blast during a four-on-four sequence in the second.

“Holts was a stud,” Capitals forward Brooks Laich said. “He was a stud throughout the game. He made some tremendous saves. They had some great looks where, we saw it from the bench, we thought it was going in and he was able to get a pad across and then came up big in the shootout.”

Evgeni Nabokov was Holtby’s equal, making 21 stops. Kyle Okposo’s one-timer with 4:59 to play in regulation forced overtime and assured that both teams would emerge with something.

“The guys will enjoy it for a little bit, but we’ve got a lot of hockey left,” Washington coach Adam Oates said. “I think it’s more important that we focus on the [games this] weekend because it obviously can drop just as fast.”