Cassel and Chris Chambers hooked up on the long completion in overtime, setting up Succop's winning kick.
The Chiefs ended a 10-game losing streak at home.
Cassel completed 15-of-30 passes for 248 yards, including touchdown throws of 21 yards to Leonard Pope and 2 yards to Jamaal Charles, who also scored on a 97-yard kickoff return to open the game.
Ben Roethlisberger passed for three touchdowns for the Steelers (6-4) and finished with 398 yards on 32 completions in 42 attempts.
Roethlisberger's scoring throws were for 8 yards to Hines Ward, 10 yards to Heath Miller and 8 yards to Rashard Mendenhall.