The Flyers’ Carter Hart and Washington’s Braden Holtby have known each other for several years, having been introduced by their sports psychologist, John Stevenson.

The rivals have become friends, and on Wednesday, they went head-to-head in an old-fashioned goaltenders’ duel.

Advantage, Holtby.

Barely.

Evgeny Kuznetsov scored what proved to be the winner in the shootout as the Capitals outlasted the Flyers, 2-1, at the Wells Fargo Center.

Washington, which had a 2-1 edge in shootout goals, ran its point streak to 13 games (11-0-2).

The Flyers, who got a goal from Claude Giroux in the third period and another in the three-round shootout, overcame a slow start and increased their point streak to seven games (5-0-2).

Hart made 35 saves and was the No. 1 reason the Flyers salvaged a point, though their four-game winning streak was snapped. The Caps lead the league in goals (four per game) and they had not scored fewer than three goals since Oct. 5.

“He was on tonight,” defenseman Matt Niskanen said of Hart. “He was really good, probably our best player throughout the game. Gave us a chance to make a push in the second.”

Sean Couturier hit the post with 1:46 to go in overtime and later was twice denied by Holtby in front.

With just under a minute left, Alex Ovechkin shot wide on a breakaway.

Welcome to the Flyers’ third straight shootout. (They went past regulation for the sixth time in their last seven games.)

Early in the third period, Jake Voracek went around defenseman Radko Gudas -- who was playing his first game against the Flyers since they traded him to Washington for Niskanen last June -- and created a two-on-one down low. Giroux turned into a power-play goal, knotting the score at 1-1 with 13:22 left in regulation.

Hart made a tough save on John Carlson from in close with 3:54 left in regulation. Less than a minute later. he calmly stopped Tom Wilson from point-blank range.

With 31 seconds left in regulation and Wilson in alone, Hart got a piece of Wilson’s shot and it trickled wide.

The Caps had a 36-31 shots edge, and both goalies were superb.

Hart entered the night having won four straight and compiling a 1.91 GAA and .929 save percentage in that span.

The Flyers were unable to generate much attack time, so coach Alain Vigneault put his lines in a blender and mixed them up early in the second period. He made changes to three of the four units, with only the Oskar Lindblom-Couturier-Travis Konecny line remaining intact.

“I just felt that a couple of our guys were working hard and some were fighting it," Vigneault said. “I was looking for nine workers.”

Among the new lines: Giroux centering Voracek and Michael Raffl, a unit that was together a few years ago. They played well when reunited Wednesday.

After Vigneault made the changes, “we tilted the ice their way,” center Kevin Hayes said.

The Flyers had several golden chances late in the second period.

Just after their power play expired, Konecny had Holtby beaten from the high slot, but his shot kissed off the right post with a little less than five minutes left in the second.

A short time later, Holtby made a great save to turn aside Travis Sanheim’s tip-in attempt in front.

“We bounced back in the second and third and generated lots of chances,” Hart said. “That was kind of the message AV [Vigneault] had for us after the first.”

The Capitals dominated virtually every aspect of the game as they built a 1-0 first-period lead on a goal by left winger Brendan Leipsic.

Washington won most of the board battles, had its forecheck frustrating the Flyers, and spent most of the opening period in the hosts’ end, outshooting them, 16-5.

“They gave it to us in the first,” Hayes said. “That wasn’t how we should have come out.”

Leipsic, whose fourth line was matched against Hayes’ original unit with Voracek and Carsen Twarynski, scored on a rebound of a Carlson shot, putting the Caps ahead, 1-0, with 13:47 remaining in the first.

The Flyers were coming off back-to-back road victories over Toronto and Boston, winning each game in a shootout.

But this was their supreme test, facing a Washington team that has not lost in regulation since Oct. 14. The Flyers regrouped after the first period -- outshooting the Caps, 26-20, the rest of the way -- and got a point. That gave them nine out of a possible 10 points in their last five games.

“It’s a lot to build on,” Voracek said.

“They’re the top team in the league right now," Hart said of the Caps. “They’ve been rolling, and for us to be right there with them shows we can be in there with any of the top teams in the league.”

Breakaways

Ivan Provorov collected an assist and led the Flyers in shots (4) and time on ice (25:06). ... Sanheim had four giveaways. ... Joel Farabee played just one shift after the second period. “Joel was fighting it a little bit tonight and that’s a pretty big team and a pretty good team with a lot of experience,” said Vigneault, who plans to give the rookie a lot more action Friday in Ottawa. ... It’s the first time the Flyers have had six out of seven games go beyond regulation since the league went to overtime in 1983-84, according to the NHL.