The AFC West sides were evenly matched throughout four quarters at the Allegiant Stadium, despite the Raiders losing starting QB Derek Carr late in the first quarter.
Backup Marcus Mariota did not need long to get going, completing a 35-yard pass to Darren Walker in the second quarter to put the home side up 10-7.
The scores were levelled towards the end of the half when Michael Badgley made a 22-yard field goal, but Chargers quarterback Justin Herbert found Tyron Johnson for a score and a 17-10 half-time lead.
Both sides traded a touchdown in the fourth and Mariota led a 19-play drive later in that quarter, capped off with a two-yard rushing TD as the sides finished 24-24 in regulation.
The Raiders could only manage a field goal on their drive, and Herbert went on to complete a 53-yard pass to put the Chargers within sight of the end zone as he sealed the game with a one-yard rush.