Down four points with 1:22 remaining, Philip Rivers marched down the field and connected with Seyi Ajirotutu from 26 yards out for the winning touchdown and his lone reception of the game.
The loss capped off a season high for Kansas City (9-2) in points scored and allowed.
Alex Smith completed 26 of 38 passes for 294 yards and three touchdowns. He tossed one interception in the third quarter, leading to one of Danny Woodhead's two touchdowns and the second of seven lead changes in the second half.
Already playing without starting offensive linemen Erich Fisher and Jon Asamoah plus defensive end Mike Devito, the Chiefs lost both outside linebackers Tamba Hali and Justin Houston in the first half. Both suffered sprains, Hali to his right ankle and Houston to his left shoulder, per Andy Reid, and will undergo MRI on Monday. Those losses affected the pass rush again as Eric Berry mustered the team's only sack of the day in the fourth quarter.
Kansas City, down 3-0 late in the first quarter, scored 14 unanswered points with a 32-yard hookup between Smith and Donnie Avery and a seven-yard run from Jamaal Charles.
Charles punched in two touchdowns and racked up 115 yards on 14 carries.
Rivers completed 27 of 39 passes for 392 yards and three touchdowns as the Chargers (5-6) gained almost 500 total yards.