The Kings moved to 4-0-2 on their current 10-game road trip, which continues through Columbus, both New York teams and Anaheim through Feb. 23. They snapped a three-game winning streak for the Eastern Conference-leading Flyers.
Quick, who sat out Saturday's 4-1 win over the Washington Capitals, was sharp in the Sunday matinee. He covered up a loose puck with 8:28 left in the game after Danny Briere had fanned on a Jeff Carter pass in the goal mouth.
Flyers defenseman Chris Pronger also hit the post with a shot in the first period.
A turnover by Mike Richards behind the net led to Doughty's goal. The defenseman fired a one-timer from the top of the slot past rookie goalie Sergei Bobrovsky.
Anze Kopitar assisted on the goal, his 19th point in the previous 23 games.
The Kings had a chance to go up 2-0 minutes later, but Bobrovsky did a split to deny Wayne Simmonds on the right side. Bobrovsky stopped 24 shots.
Quick helped the Kings improve to 18-0 when leading after two periods and recorded his sixth shutout of the season, tying him for third in the league with Montreal's Carey Price. It's also his second in six starts.
Despite outshooting the Kings 40-25, the Flyers were shutout for the fifth time this season. They also were blanked in Tampa Bay on Feb. 1, which was also their last defeat before Sunday.
NOTES: The Flyers are 82-37-15-2 all-time vs. Los Angeles. ... Kopitar played in his 312th consecutive game.