Rivers also threw scoring passes of 10 yards to Jackson and 2 yards to Kris Wilson, finishing with 24 completions on 36 throws for 209 yards. He was intercepted twice.
LaDainian Tomlinson was held to 22 yards in 12 carries for the Chargers (5-3), who have won three straight games.
Eli Manning passed for 215 yards, including touchdown throws of 6 yards to Steve Smith and 8 yards to Kevin Boss for the Giants (5-4). Manning had 25 completions in 33 attempts.
Lawrence Tynes kicked 38- and 22-yard field goals for New York, which has lost four straight games after a 5-0 start.