Bryzgalov earned his third shutout of the season, and the 26th of his career, even though the Flyers were missing two defensemen who sat out with injuries: Kimmo Timonen and Andrej Meszaros.
Capitals captain Alex Ovechkin, a two-time league MVP, played fewer minutes than most of Washington's other forwards and was held without a goal for the seventh time in his last 10 games. Washington has lost two games in a row - both at home, both shutouts - following a three-game winning streak.
Buoyed by a raucous group of Flyers fans in the stands, Philadelphia moved within two points of the Pittsburgh Penguins for fourth place in the Eastern Conference. Washington, meanwhile, remained stuck in ninth in the East, one spot out of the playoff picture.
It was an eventful, if scoreless, first period.
About 5 1/2 minutes into the game, Capitals forward Troy Brouwer decked Erik Gustafsson along the boards, then fought Scott Hartnell. Both Brouwer and Hartnell were sent to the penalty box. A few minutes later, there was a near-skirmish right in front of Bryzgalov, with a half-dozen players pushing and shoving and yammering before the officials separated them.
Without Timonen and Meszaros - both out indefinitely with what the Flyers said are lower-body injuries - Bryzgalov needed to play well, and he did.
Making a sixth straight start, Bryzgalov was tested frequently, including when he made saves on shots by Alexander Semin and Mathieu Perreault in quick succession during the first period. About 7 minutes into the second, Capitals forward Mike Knuble broke behind the Flyers defense for a 1-on-1 chance, but Bryzgalov kicked the puck aside.
Right after that, Laviolette called time and gave his players an animated talking-to, gesturing all the while.
Sure enough, less than a minute later, the Flyers reacted by taking the lead at the 7:51 mark on left wing Wellwood's second goal in six games this season. That ended a dubious streak: In each of the Flyers last nine games, they had allowed the first goal.
In Philadelphia's previous outing, at home Thursday, it trailed the New York Islanders 1-0 after only 95 seconds, prompting Laviolette to call time and rip into his players. Worked that night, too: The Flyers came away with a 6-3 victory.
NOTES: As usual, Washington's fans booed any time former Capitals forward Jaromir Jagr touched the puck. Jagr played in Washington from 2001-04. ... Sitting out Sunday ended Timonen's streak of consecutive games at 248, the Flyers' longest active run. ... The Capitals recalled G Braden Holtby from Hershey of the American Hockey League as an emergency backup, because Tomas Vokoun has a lower-body injury. The last time Holtby was brought up to Washington, on Feb. 13, he played for the only time this season and lost to San Jose 5-3. ... Philadelphia's next game is at home on Tuesday against the Detroit Red Wings. ... The Capitals host Carolina on Tuesday night. ... Philadelphia has won two of three games against Washington this season; they finish the series March 22 at Philadelphia.