Philadelphia Flyers right wing Wayne Simmonds has little room to maneuver between Capitals goalie Braden Holtby, left, and defenseman Nat Schmidt. (Ton iL. Sandys/The Washington Post)

It was only his second shift of the third period when Philadelphia Flyers forward Wayne Simmonds finally lost control Sunday afternoon.

A blocked shot and a check into the boards by Washington Capitals defenseman Nate Schmidt had thwarted Simmonds’s latest foray to net and the Flyers’ leading goal scorer was flustered. He skated toward the home bench at Wells Fargo Center and began repeatedly banging the butt of his hockey stick against his head.

This image of irritation, more than the highlight-reel goals of years past, will define the manner in which the Capitals beat Philadelphia, 1-0, in Game 6 to finish off this best-of-seven Eastern Conference quarterfinals series and advance in the Stanley Cup playoffs.

Washington gave up six goals over six postseason games against the Flyers (and one came on an empty net to close Game 5), which is a franchise record for fewest goals allowed in a seven-game playoff series. But even as goaltender Braden Holtby continued his strong play with two shutouts, including a 26-save performance Sunday, it was the overall defensive effort that left an indelible mark.

“They did a good job of closing us off and they obviously played great,” Simmonds said when asked about his Game 6 antics on the bench. “It’s just a little bit of frustration in all that noise.”

Neither Simmonds nor captain Claude Giroux, Philadelphia’s leading point scorer during the regular season, scored a goal against Washington in the series, the result of a well-executed plan and defensive synergy throughout the lineup.

The Capitals’ strategy centered around cutting off the time and space for Philadelphia’s forwards, but the straightforward approach took a “team commitment,” according to blue-liner Matt Niskanen. Forwards had to back-check, forecheck and block shots. The defense, meanwhile, mostly kept the Flyers away from the front of the net, won battles along the boards and limited the shots Holtby faced.

“The games kind of call for it sometimes,” Holtby said. “We had to make sure we were sound defensively and we were.”

Coach Barry Trotz said he “challenged our top guys” about their two-way play, and frequently matched up center Nicklas Backstrom’s line, as well as the fourth-line centered by forward Jay Beagle, to stymie the Flyers’ top offensive weapons. The Capitals also killed 23 of 24 power plays over six games.

“They’re not an easy group to shut down, so it was good on us for getting them shut down,” Trotz added.

Trotz also praised the work Niskanen and defenseman Karl Alzner did together throughout the series, especially once veteran Brooks Orpik left Game 3 with an upper body injury. Niskanen, Alzner and defenseman John Carlson all played more than 25 minutes on Sunday.

In Orpik’s place, Trotz used Taylor Chorney and Mike Weber the past two games and, other than a fluky goal off Chorney’s skate on Friday night at Verizon Center, neither looked out of place. Schmidt and defenseman Dmitry Orlov, both playoff rookies this year, were not on the ice for an even strength goal the entire series.

In fact, before the Flyers’ late charge in Game 6, when Holtby made several timely saves to preserve the win, the Capitals had out-shot Philadelphia, 80-30, over the previous six periods.

“Holts obviously has to play well for our team to be successful, but we try and lessen the load as much as possible,” Alzner said. “It’s a good feeling, but we’ve got a different animal coming up next.”

Indeed, the Penguins will bring a more potent power play and more top-end weapons when they meet Washington in the postseason for the first time since 2009 starting later this week. For now, however, the Capitals were content to savor the defensive stand that got them back to the Eastern Conference semifinals.

As Niskanen put it after Game 6 Sunday: “Only got one goal, but that’s all it took.”