With Monday night's 21-14 final, San Diego's winning streak against the Chiefs ended at five games.
The Chargers managed only one touchdown in the second half. And that was on a gift.
On the final series, Rivers' first pass was incomplete, then Darren Sproles lost 2 yards on a stalled run. Another pass from Rivers sailed high. Then, with 39 seconds left, Rivers missed on fourth down, clinching the Chiefs' first Monday night victory in a decade.
"They made some big plays in all three phases," Chargers coach Norv Turner said. "They handled the environment in terms of the weather conditions. I thought they did a good job in handling that, particularly in the second quarter.
"The disappointment for me comes obviously from our (kick) coverage teams. We think that should be a strength for us and something we work hard at."
Jamaal Charles had a 56-yard touchdown run after Rivers' 3-yard TD pass to Antonio Gates put the Chargers on the board first. Then, rookie Dexter McCluster, a training camp sensation with quickness and flair, broke a team-record by one yard with a 94-yard punt return for a 21-7 halftime lead.
"That's the longest of my career at any level," said McCluster. "What better time than that -- Monday night football in Arrowhead. You couldn't ask for a better time."
Ryan Mathews, in his NFL debut, had 75 yards on 19 carries for the Chargers.
Rivers was 22 for 39 for 298 yards and two touchdowns. Matt Cassel, with a history of playing poorly against the Chargers, was 10 for 22 for 68 yards, including a 2-yard TD pass following a San Diego turnover.