The Raiders took the lead in the third play from scrimmage as Derek Carr lofted the ball deep for wide receiver Andre Holmes, who beat his man and ran all the way into the endzone for the 77-yard score.
San Diego hit back immediately as Rivers produced a solid drive before he hit Eddie Royal on a deep fade route, and the receiver snagged the ball over a defender for the 29-yard touchdown.
The Chargers upped the ante in the second quarter and Rivers once again moved them the length of the field, and then found Malcom Floyd over the middle on a slant route for a five-yard score.
Oakland rallied and Carr produced a series of excellent throws to move his side into a scoring position in the red zone before firing a touchdown strike over the middle for James Jones.
Sebastian Janikowski had the chance to fire the home side ahead just before the break with a 53-yard field goal, but he dragged his effort wide of the uprights.
In the second half, the Raiders took advantage of a miscued special teams play by the Chargers to earn good field position. This allowed Carr to hit Brice Butler over the middle, and the receiver ran 47 yards to the endzone.
San Diego managed to respond to the setback as Rivers moved the ball seamlessly downfield before he connected with his tight end Antonio Gates in the endzone for a five-yard score.
However, Carr was not to be stopped as he put his team back into the lead courtesy of a methodical drive, which culminated in the rookie finding Holmes in the endzone for his second score of the game.
The Chargers were then held to a field goal in response from Nick Novak, but then Rivers engineered the game-winning drive as Branden Oliver ran in from one-yard out. Carr had the chance to level the scores late on but was intercepted by Jason Verrett to seal the visitors' victory.