Rivers finished the game completing 18 of 29 passes for 178 yards and a touchdown.
"Philip is the best in the business," Chargers coach Mike McCoy said. "He's been that way for a long time ... He's a special player."
It wasn't the first time Rivers set a team record. The five-time Pro Bowler already holds team records for quarterback wins (93), passing completions (3,579) and passing touchdowns (292).
Before the game, Rivers, 34, said passing Fouts wouldn't be lost on him.