Alex Ovechkin scored, and Charlie Lindgren made 27 saves in his second start of a back to back for the Capitals (40-31-11), who won four of their final five games to clinch the second wild card from the Eastern Conference; they will face the New York Rangers in the first round. Lindgren made 16 saves in a 2-0 win against the Boston Bruins on Monday.
The Capitals finished the regular season tied for points (91) with the Red Wings, who defeated the Canadiens 5-4 in a shootout, but owned the tiebreaker based on regulation wins (32 for Washington, 27 for Detroit).
It's the ninth playoff berth in 10 seasons for Washington, which missed qualifying last season for the first time since 2013-14.
"Unreal," Ovechkin said. "We fight through lots of stuff that happen at deadline, injuries ... but I think the belief inside the locker room was tremendous. We enjoyed that process. It's special. That's why we play hockey. You want to be in that type of atmosphere, you want to be in, and we beat pretty good teams to be able to make it."
Erik Johnson scored for the Flyers (38-33-11), who were eliminated from playoff contention after losing nine of their last 11. Ersson made 16 saves.
"This was a high-stakes game," Philadelphia coach John Tortorella said. "Started off very tentative, but then I felt we got on the attack. Give them credit. They defended well. They defended a lot. And we just couldn't find our way."
The Flyers had been in a playoff position for most of the season, but lost eight in a row (0-6-2) from March 24-April 9 to fall out of a spot.
"From the start of the year, I think everyone was counting us out," Philadelphia forward Scott Laughton said. "Probably had that eight-game losing streak at the worst time of the year. Couldn't really regain ground and that's what cost us."