Pryor completed 18-of-23 passes for 221 yards and rushed 11 times for 31 yards. He sat out the Raiders' loss to Washington last week.
Denarius Moore helped the Raiders (2-3) end a two-game losing streak by catching five passes for 84 yards and a touchdown. Teammate Rod Streater hauled in three passes for 56 yards and a score.
Rashad Jennings, subbing for the injured Darren McFadden, rushed 10 times for 41 yards.
The Chargers' offense turned over the ball five times, including three interceptions thrown by Philip Rivers, who was 36-of-49 for 411 passing yards and two touchdowns.
Keenan Allen had six receptions for 115 yards and a TD, and Vincent Brown had eight catches for 117 yards for the Chargers (2-3).
San Diego produced 32 rushing yards after running back Ryan Mathews left the game in the second quarter with a concussion.
The game didn't start until 8:35 p.m. PDT start to allow O.Co Coliseum workers time to switch the field from baseball to football following the Oakland Athletics' playoff game Saturday night.