The berth comes one season after Kansas City (11-3) finished a leage-worst 2-14.
Charles scored four of his touchdowns through the air, making him the first running back in NFL history to do so in a single game. He caught eight balls for a game-high 195 yards. His other score came on a one-yard run in the second quarter.
Alex Smith completed 17 of 20 passes for 287 yards and five touchdowns and a fumble. Sean McGrath caught Smith's final score on a six-yard connection late in the third quarter.
The Chiefs defense intercepted Matt McGloin twice and Terrelle Pryor once, with Eric Berry taking one of his two picks 47 yards in the first quarter to give Kansas City a 21-3 lead. Frank Zombo, Derrick Johnson, and Ron Parker also tallied interceptions.