It was Succop's second successful kick of the day and made up for a missed chance to win the game earlier in the overtime, when he shanked a 39-yard attempt wide left.
Jamal Charles gained 177 yards on 22 carries and caught four passes for 61 yards for Kansas City (5-2), while Matt Cassel went 14-of-26 in the passing department for 152 yards and a touchdown.
Buffalo (0-7) remained winless with its second straight overtime setback. Ryan Fitzpatrick went 24-of-48 passing for 223 yards, including a touchdown and an interception, for the Bills.
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