Nicklas Backstrom had a goal and an assist for the Capitals (2-5-1), which had lost two straight.
The Capitals and Flyers were tied 1-1 after two periods.
"I think the last couple of games in the third period we seemed to break down and get away from what we want to be doing in the neutral zone," Wolski said. "I think tonight we really stuck together and reminded each other to stay wide. We got a lot of turnovers and pucks going the other way."
"We just weren't good enough, especially in the third period when it was 1-1," Schenn said. "You have to learn how to win those hockey games, and to give up two, it's obviously not what we were looking for."
Brouwer's third goal of the season at 3:57 of the third period put the Capitals ahead for good. He took a pass in the left circle from Mike Green, waited a few seconds, and wristed a shot over goalie Ilya Bryzgalov's shoulder.
"I was looking to pass for the longest time," Brouwer said. "Then I saw that I had a little bit of room on the short side, so I figured I might as well take it."
Less than three minutes later, Wolski poked the puck away from defenseman Luke Schenn at the blue line, skated in alone, and beat Bryzgalov to make it 3-1.
"It's turnovers," Flyers coach Peter Laviolette said about what went wrong in the third period. "But we need to compete better, as well."
The Flyers got back within a goal with 9:30 remaining when Brayden Schenn beat Holtby with a shot from the left circle.
The Capitals held on behind Holtby, who made his first start since Jan. 22. Bryzgalov finished with 23 saves.
The Flyers took a 1-0 lead when Gervais knocked a loose puck past Holtby at 11:43 of the second period for his first goal with Philadelphia.
Washington tied it six minutes later. John Carlson poked the puck from Sean Couturier right to Backstrom, who was trailing the play. Backstrom broke in alone and lifted a backhanded shot over Bryzgalov's glove with 2:18 remaining in the second.
"I think our line played a little bit better," Backstrom said. "We passed the puck a little bit better and we created more chances, too."
The Capitals, who came in off a 3-2 loss on Thursday at Toronto, dominated early against Philadelphia -- which hadn't played since losing at the New York Rangers on Tuesday.
Midway through the first period, the Capitals held a 10-2 edge in shots, but Bryzgalov kept the game scoreless. He made several tough saves, his best on a backhand attempt off the stick of Alex Ovechkin, who was alone in front after a feed from Wolski.
"I thought it was the best game he's played this year," Capitals coach Adam Oates said of Ovechkin. "He was involved the whole game. He had a lot of opportunities."
Late in the first period, Washington's John Erskine caught Wayne Simmonds in the face with an elbow that sent Simmonds to the ice with a bloody nose.
"It looked dirty when I first saw it. A tough hit," Laviolette said.
No penalty was called, but Simmonds didn't return to the game.
"Obviously, he's got a head injury and probably a little bit of whiplash going on right now," Flyers general manager Paul Holmgren said. "He seemed OK after the game. We're just going to have to wait and see how he is (Saturday)."
The Capitals didn't make Erskine available to the media after the game.
The Capitals were 0 for 5 on the power play. The Flyers were 0 for 3. ... Former Capitals forward Mike Knuble made his return to Washington. The 40-year-old Knuble, who spent the previous three seasons with Washington, signed with Philadelphia on Jan. 25.
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