Carr had his way with the Chargers' defense all game, beginning with the opening drive. The rookie out of Fresno State found receiver Andre Holmes, who exploded with a long catch and run for a touchdown. The 77-yard strike was the Raiders' (0-5) longest play from scrimmage this season.
Phillip Rivers answered back on the ensuing drive by connecting with Eddie Royal for a 29-yard score to tie it 7-7.
Both teams traded touchdowns again in the second quarter. Rivers' five-yard toss to Malcom Floyd was followed by Carr's six-yarder to James Jones that tied the game 14-14.
Oakland blew an opportunity to take the lead into halftime when Sebastian Janikowski's 53-yard field goal went wide left during the closing seconds.
After the Chargers turned the ball over on downs, the Raiders ended their first drive of the second half with a 47-yard touchdown catch by former San Diego State receiver Brice Butler, giving them a 21-14 lead.
Rivers came through again on the following drive. Needing just 8 plays, he found Antonio Gates in the end zone for the duel's 66th career touchdown connection to tie the game 21-21 to end the third quarter.
After back-to-back three-and-outs, Carr connected with Holmes again for a six-yard touchdown in the corner of the end zone, giving the Raiders a 28-21 lead with 10:01 left to play. It was the first time the Chargers' allowed an opponent to score in the fourth quarter since week one.
After settling for a 30-yard field goal by Nick Novak, the Chargers, trailing 28-24, prevented the Raiders from extending their lead (and most likely sealing the game) after forcing a much needed three-and-out.
The Bolts capitalized with a six-play drive that ended with a one-yard go-ahead touchdown leap by rookie running back Branden Oliver, who finished with 26 carries for 101 yards.
For Rivers, it was the 21st game-winning drive of his career, and the fourth against the Raiders.
With their fifth straight win, the Chargers return to Qualcomm Stadium next week to host the Kansas City Chiefs in another AFC West match-up.