Malcom Floyd touched down from Philip Rivers' six-yard pass and Nate Kaeding kicked five field goals to give the Chargers a well-deserved victory.
The Raiders were hoping to get Allen's tenure of to a positive start but were largely repelled by a stoic San Diego defence.
The Chargers did enough to win on a night they started undrafted rookie Mike Harris at left tackle and were missing starting running back Ryan Mathews and receiver Vincent Brown to injuries.
San Diego protected Harris by throwing short often with 16 of Rivers' 24 completions going to running backs and tight ends. Rivers threw for 231 yards, but was sacked just once and did not turn the ball over after having 20 interceptions a year ago.
Early in the third quarter, the Raiders lined up to go for it on fourth-and-2 from the San Diego 48. But after a penalty for 12 men in the huddle, Oakland decided to punt. Goethel's snap rolled back to Lechler, who was tackled for a loss, giving San Diego the ball at the Raiders 39. That set up a 28-yard field goal by Kaeding.
After Oakland was stopped on its next drive, Lechler set up closer to Goethel, whose snap made it back in the air.
The Chargers once again had to settle for a short field goal and led 16-6 heading into the fourth quarter.
Goethel rolled another snap back early in the fourth quarter, once again giving San Diego the ball in Oakland territory, setting up Kaeding's career-high tying fifth field goal to make it 22-6.
Palmer finally got Oakland into the end zone with 54 seconds left on a 2-yard pass to rookie Rod Streater and the two connected for a 2-point conversion to make it 22-14. But San Diego recovered the onside kick and iced the game.