Niklas Backstrom had a goal and an assist for Washington (2-5-1), which had lost two straight.
Defenseman Bruno Gervais, and Brayden Schenn scored for the Flyers (2-6), who have lost three in a row.
Brouwer's third goal of the season at 3:57 of the third snapped a tie and put the Capitals ahead for good. He took a pass in the left circle from Mike Green and wristed a shot over goalie Ilya Bryzgalov's shoulder.
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.
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 the Flyers.
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.
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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.
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. No penalty was called, but Simmonds didn't return to the game.
Before the ensuing faceoff, Philadelphia's Zac Rinaldo fought Matt Hendricks. Both players were ejected from the game.
NOTES: 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, and signed with Philadelphia on Jan. 25.
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