After finishing off the Flyers in Game 6 of the Eastern Conference First Round, the Capitals could finally exhale and get ready for a star-powered second-round matchup with Sidney Crosby and the Pittsburgh Penguins.

PHILADELPHIA -- In the moments following the Washington Capitals' 1-0 victory against the Philadelphia Flyers Sunday, the sound of clapping and some cheering could be heard in the hallway outside the celebratory visiting locker room at Wells Fargo Center.

As the Presidents' Trophy winners, they had done what they were supposed to do by eliminating the Flyers, who entered the Stanley Cup Playoffs as the second wild card in the East. It was far from easy, though.

At least, it wasn't as easy as it appeared it might be after they won the first three games of the best-of-7 series.

Video: PHI@WSH, Gm5: Neuvirth backstops Flyers in 2-0 win

As much as the Capitals talked Sunday about knowing beforehand this would be a long series, after they went up 3-0, they wanted to get that fourth win as quickly as possible. With Flyers goalie Michal Neuvirth, the former Capital, taking over in net, the scrappy Flyers pushed the series to six games.

Neuvirth frustrated his former teammates by stopping 75 of the 76 shots he faced in winning Games 4 and 5, but the Capitals stayed with it and Nicklas Backstrom finally broke through with a goal 8:59 into the second period. That would be all they needed on this day with goalie Braden Holtby making 26 saves for his second shutout of the series.

"The fourth one is the hardest one," Capitals captain Alex Ovechkin said. "They didn't give us any easy games. They were all over us. They won two games in a row and probably felt pretty good about themselves, but we found a way to win the game."

For the time being, the Capitals quieted the questions they faced over the previous two days about their inability to finish off a playoff series. They wanted no part of a Game 7 at Verizon Center on Wednesday, which would have had them on the verge of becoming the fifth team in NHL history to blow a 3-0 series lead, and they played like it Sunday.

Video: Capitals win Game 6, 1-0, to advance to Round 2

"Yeah, we were disappointed that we lost the last two, but we got it together and played a good team game," Backstrom said. "It's a tough arena to play in, but I think we played a really good team game."

Actually, they might have played even better in their 2-0 loss in Game 5 on Friday, a game in which they outshot the Flyers 44-11, but were not rewarded with a goal. The positive sign Sunday was that the Capitals were undeterred by that happened Friday and kept playing the same way.

"It shows we can win games in a lot of different ways, I think, and it shows a lot of character and we never quit," Capitals forward Marcus Johansson said. "We stick together and stick up for each other and we find ways to win. That's something you need going forward here."

Maybe the Capitals of the past would have wilted under the pressure they faced heading into Game 6, but this group was able to battle through it and, possibly, come out the other side better for having gone through it.

"We know that we can battle through some adversity. That's been probably our calling card this season," Capitals defenseman Karl Alzner said. "We've been able to fight back in games and play hard no matter what the situation and we showed that in this series. We just had to look at things the right way. We were up 3-2 going into Game 6. Like Barry told us [Saturday], if someone had told us that before the series started that you're up 3-2, you're going to take that, you're happy about that.

"It's just the fact that the way it happened people were a little bit panicky and we weren't."

The Capitals may not have been "panicky", but there was pressure on them because of their past troubles in clinching situations, including a 1-8 record in their nine previous chances to close out a series.

"Especially between Game 5 and Game 6, that's a tough thing to go through as a team and we showed our character in here," Holtby said. "Every piece of experience you can gain will help you in the long run."

The Capitals still intend for this to be a long run and getting past the Flyers was just the first step. Taking the next one is likely to be even more difficult in a long-awaited second postseason series between Ovechkin and Crosby.

"It's going to be an interesting series," Ovechkin said. "It's going to be a hard series. Two good teams play against each other and we'll see what's going to happen."

When asked what he remembered about his first postseason meeting with Crosby in the second round of the 2009 playoffs, Ovechkin quickly replied, "nothing."

It was a seven-game battle that included a Game 2 in which Ovechkin and Crosby each had hat tricks. After six tight games, the Penguins prevailed 6-2 in Game 7 and advanced to eventually capture the Stanley Cup. The Capitals are still seeking their first appearance in the Eastern Conference Final since their run to the Stanley Cup Final in 1998.

This year, the Penguins appear to be the biggest obstacle blocking the Capitals' path out of the Eastern Conference. They were the NHL's hottest team in the second half, going 33-8-5 after a 2-1 loss to Carolina on Dec. 19 left them at 15-14-3.

Despite being without No. 1 goalie Marc-Andre Fleury because of a concussion, the Penguins have not slowed in the playoffs and, with rookie Matt Murray in net for the final three games, dispatched the New York Rangers in five in the first round.

Video: PIT@NYR, Gm4: Murray shuts out Rangers in Game 4

After the Capitals were able to shut down the Flyers' top players such as Claude Giroux (one assist), Wayne Simmonds (two assists) and Jakub Voracek (one goal), facing Crosby, Evgeni Malkin, Phil Kessel and Kris Letang at the top of their games and a much deeper Penguins' lineup will present a whole new set of challenges.

"It's a good feeling," Alzner said of beating the Flyers, "but we've got a different animal coming up next, so it will be interesting."