"Sometimes you need your goalie to bail you out," said center Brayden Schenn, another former King.
Simmonds, playing in Los Angeles for the first time since he was traded to the Flyers in 2011, scored his 100th career goal and 18th of the season. He also added an assist on Claude Giroux's game-icing, power-play goal with 1 minute, 58 seconds left in the game.
"These are two big points we needed to get," said Simmonds, downplaying that the win - and his two-point game - came against the team that traded him.
With about three minutes remaining and the Kings facing a 1-0 deficit, former Flyer Justin Williams hit the left post on a wraparound attempt. A little over a minute later, Giroux converted a Scott Hartnell pass for his third goal in the last four games.
The Flyers were outshot, 35-13.
"We kept them to the outside," said Mark Streit, part of a defense that was revamped because Kimmo Timonen missed the game with an injury. "They didn't have too many dangerous shots."
And when they did, Mason stood tall.
"They started coming hard at us in the second and third," Mason said.
Simmonds, an alternate captain because of Timonen's absence, took a slick pass from Vinny Lecavalier and slammed a close shot into an open net with 12:12 left in the second period, giving the Flyers a 1-0 lead. Kings goalie Jonathan Quick, who will represent the United States in the Olympics, was bumped into by teammate Jake Muzzin and unable to get back to the right side of the net.
"I was back door, and Quickie likes to challenge a lot, so he was out," said Simmonds, noting that the goalie was expecting Lecavalier to shoot from the other side. "So when I got the puck, I knew I had a lot of time."
The Kings controlled the rest of the period, but couldn't solve Mason. Los Angeles had a 14-5 shots edge in the second.
Mason was especially effective with about 3:30 to go in the second, stopping three quick shots during the Kings' best offensive flurry of the game, including a point-blank drive by Slava Voynov.
The Flyers, who played relatively well in a 5-3 loss to powerful Anaheim on Thursday, conclude their three-game trip Monday in San Jose.
"I know we didn't create a lot offensively, but we capitalized on the power-play goal, which was huge," coach Craig Berube said. "I like the battle. I like the competitiveness of the team right now."
Timonen sidelined. Kimmo Timonen missed the game with a bruised left foot, suffered when he blocked a shot in Tuesday's 5-0 home victory over Detroit. The 38-year-old defenseman played Thursday and committed a turnover that led to a shorthanded goal for Anaheim.
Andrej Meszaros replaced Timonen, who had played in all 55 games.
Breakaways. Zac Rinaldo led the Flyers with six hits. . . . Meszaros was paired with Streit, Braydon Coburn was with Nick Grossmann, and Luke Schenn was with Erik Gustafsson. . . . Mike Richards has one goal in his last 32 games.