Bush's score put the Raiders up 17-10 with 2:26 left in the third quarter and Jacoby Ford added a 10-yard scoring run in the final stanza for Oakland (8-8), which swept all six of its games against AFC West opponents this season.
But the Raiders also became the only team since the AFL-NFL merger to do so and not make the playoffs -- they dropped all six games against non-divisional opponents.
Bush finished with 137 yards on 25 carries and Jason Campbell went 15-of-25 passing for 155 yards and one touchdown for the victors.
Matt Cassel suffered a pair of fourth-quarter interceptions for Kansas City (10-6), including one returned by Stanford Routt for a touchdown.
Cassel ended with 115 passing yards as the playoff-bound Chiefs lost at home for the first time this season.