Kansas City took a 10-0 lead late in the second quarter after Chase Daniel's pass to Dwayne Bowe was fumbled at the goal line and recovered in the end zone by tight end Travis Kelce. The Chiefs went the entire season without completing a touchdown pass to a wide receiver.
The Chargers answered back with a one-yard touchdown run by Branden Oliver, that was set up by Rivers' 44-yard strike to Eddie Royal.
With the Chargers unable to score in the second half, three unanswered field goals by Cairo Santos was all the Chiefs needed to seal the win.
Had the Cleveland Browns pulled off an upset over the Baltimore Ravens, Kansas City would have clinched the sixth seed.
Rivers finished with 291 yards to put him over the 4,000-yard mark for the sixth straight season. Oliver led the ground game with 14 carries for 71 yards and a touchdown.