Making his 100th career start, Rivers surpassed the 25,000-yard mark passing while improving to 28-10 against other members of the division. He's also 9-4 against the Chiefs.
Jackie Battle had a pair of scores against his former team, and Eddie Royal also caught a touchdown pass. San Diego improved to 8-2 in its last 10 meetings with Kansas City.
Matt Cassel threw for 251 yards and two touchdowns for the Chiefs (1-3), but he had three first-half interceptions. Jamaal Charles, who followed his big game last week at New Orleans with touchdowns rushing and receiving, also fumbled twice.
Dwayne Bowe had seven catches for 108 yards and a touchdown for Kansas City.
In last season's meeting at Arrowhead Stadium, the Chargers gave the game away. The teams were tied in the closing seconds when Rivers fumbled a snap, preventing San Diego from attempting the winning field goal.
The game went to overtime and the Chiefs ultimately prevailed.
The regular officials were back on the field Sunday, and both teams kept referee Bill Leavy's crew busy. They combined for 15 penalties for 150 yards.
Chiefs safety Eric Berry was flagged twice for pass interference on the Chargers' opening possession, and Rivers capped off a 76-yard drive with a rather elementary pass to Royal for the touchdown.
Then the cacophony of errors truly began for Kansas City.
Cassel's third pass of the game was intercepted by Eric Weddle, giving San Diego the ball at the Chiefs 28. Four plays later, Nick Novak's 25-yard field goal made it 10-0.
On the Chiefs' next possession, Charles was stripped of the ball by Takeo Spikes on the first play after a false start. San Diego took over at the Chiefs 5, and Battle pounded forward twice to give the Chargers a 17-0 lead all before Kansas City had run five offensive plays.
The Chiefs have been outscored 41-6 in the first quarter this season.
Charles fumbled again midway through the second quarter, but this time the Chargers gave it right back. Rivers underthrew Robert Meacham, and Brandon Flowers made the interception.
Kansas City managed to go 85 yards in just five plays, Charles providing the highlight on an electrifying 37-yard touchdown run. But the momentum was squandered on the its next possession, when Cassel threw well behind Tony Moeaki, and Chargers linebacker Donald Butler grabbed hold of the deflection and waltzed 21 yards untouched to give San Diego a 27-6 lead.
Cassel threw his third INT deep in San Diego territory near the end of the half.
The Chiefs put together a long drive to start the third quarter, and Charles' 13-yard TD catch with 8:40 left gave the hardy Kansas City fans still sticking around reason to believe that yet another big comeback could be at hand.
But after rallying from a franchise-record 18 points down to beat New Orleans last Sunday, the Chiefs couldn't stop giving away their chances of getting back in the game.
They went three-and-out on two straight series, and Shaun Draughn fumbled on the next.
The Chargers put a tidy bow on an easy if underwhelming victory by going 49 yards for another touchdown, this time with Rivers finding Battle out of the backfield for the score.
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