Harrison's game-winner broke a 34-34 tie with 44 seconds left and capped a fourth quarter in which the teams combined to score 24 points in a 12-minute span.
Harrison carried the ball 34 times, scoring three touchdowns and picking up a career-high 286 yards --- the third-highest single-game rishing total in NFL history and a Browns' record, eclipsing Hall of Famer Jim Brown's single-game franchise rushing total.
Premier kick returner Josh Cribbs scored on 100- and 103-yard kickoff runs, while Phil Dawson kicked two field goals for the Browns (3-11), who have won two straight.
Kansas City's Jamaal Charles scored once on 25 carries for 154 yards.
Matt Cassel threw for 331 yards and two touchdowns.
Chris Chambers scored once on five receptions for 114 yards, and Ryan Succop kicked to field goals for the Chiefs (3-11), who have lost four in a row.