Charles' 1-yard run after Tennessee linebacker Moise Fokou was flagged for an unnecessary roughness penalty capped a run of 13 unanswered Kansas City points to end the game.
Charles finished with 108 yards and Alex Smith compiled 245 more through the air for the Chiefs (5-0), who are off to their best start since 2003.
Fitzpatrick, subbing for the injured Jake Locker, passed for 247 yards with a touchdown and also rushed for a score for the Titans (3-2).
Ray Liotta sues skin care company over use of likeness
Millions of Getty images now available for free via embed tool