Dante Hall's 49-yard kickoff return set up the game-winning field goal, as Kansas City (7-8) posted its fourth straight victory.
Kerry Collins completed 18 of his 37 attempts for 217 yards and a pair of TDs for the Raiders (5-10), losers of four of their last six games.
Larry Johnson scored with 6:11 to go in the fourth quarter and the Chiefs took back the lead at 28-24. Johnson carried 25 times for 79 yards and two TDs in the win.
Sebastian Janikowski kicked a 45-yard field goal with less than four minutes as the Raiders pulled within 28-27.