Trevor Zegras and Matvei Michkov scored in the shootout, and Samuel Ersson stopped attempts by Adrian Kempe and Artemi Panarin.
Artemi Panarin’s power-play goal tied it 3-3 at 10:28 of the third period for Los Angeles on a wrist shot from the top of the left circle through Trevor Moore’s screen.
Travis Konecny and Travis Sanheim scored, and Michkov had two assists for the Flyers (33-23-12), who were coming off a 3-2 overtime win at the Anaheim Ducks on Wednesday and extended their point streak to five games (4-0-1). Ersson made 22 saves.
Philadelphia is six points behind the Detroit Red Wings for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Panarin also had an assist and extended his point streak to four games, and Quinton Byfield and Anze Kopitar scored for the Kings (28-24-16), who have alternated wins and losses over their past 11 games. Darcy Kuemper made 17 saves.
Los Angeles moved one point ahead of the Seattle Kraken and Nashville Predators, and two ahead of the San Jose Sharks for the second wild card from the Western Conference.
Byfield put the Kings ahead 1-0 at 19:31 of the first period on a wrist shot from the right circle. Byfield has three points (one goal, two assists) in his past two games following a five-game drought.
Konecny tied it 1-1 26 seconds into the second period with a wrist shot from the high slot, but Los Angeles took a 2-1 lead 21 seconds later when Kopitar tapped in Brandt Clarke’s shot, which went wide and caromed off the boards to the left post for the open goal.
Cates tied it 2-2 at 4:12 when Kuemper couldn’t cover up Michkov’s shot from the left circle through traffic, allowing Cates to knock it over the goal line.
Sanheim put the Flyers up 3-2 at 6:59 on a shot from the blue line, with Cates and Michkov picking up the assists.
Philadelphia played with 11 forwards and seven defensemen because forwards Sean Couturier (upper body), Luke Glendening (lower body) and Denver Barkey (upper body) were not available.
