The Raiders ended a two-game slide and took the lead in the AFC West at 5-4. Kansas City could move into a share of the division lead with a home win Sunday over Denver.
San Diego has dropped four in a row while falling to 4-5.
Palmer, who sat out the first half of the season before being traded from Cincinnati, gave Oakland a 17-3 halftime lead by hitting Denarius Moore with a 33-yard scoring pass with 1:51 to go in the second period.
He found Moore again with a 26-yarder in the third quarter.
The Chargers took over at their own 11 with 6:48 to go in the fourth, needing a touchdown to tie the contest. Rivers drove San Diego to the Oakland 42, where on second down he threw all the way to the end zone in an attempt to hit Vincent Jackson. Giordano, however, jumped in front of Jackson to make the interception that ended San Diego's last realistic hope.
Palmer completed 14-of-20 passes for 299 yards. Rivers was 23-of-47 for 274 yards.
San Diego's Michael Bush ran for 157 yards on 30 carries and gave Oakland the lead for good at 7-3 on a 2-yard run with 41 seconds left in the opening period.