Rivers connected on 35-of-42 pass attempts as the Chargers (2-2) got back on the winning track following a loss last week to Tennessee.
Antonio Gates rolled up 136 receiving yards with a score on 10 catches while Danny Woodhead chipped in with five grabs for 54 yards and two TDs for San Diego.
The Cowboys (2-2) dropped a second straight game despite Tony Romo's 26-of-36 passing efficiency for 245 yards and two touchdowns.
Terrance Williams hauled down seven passes for 71 yards but fumbled late in the game for Dallas.
Dez Bryant corralled two scoring passes among his six receptions for 81 yards for the Cowboys.