Fitzpatrick matched a personal best with the quartet of scoring strikes, connecting on 17-of-26 passes and finishing with 208 yards for Buffalo (1-0).
The Bills got five catches for 63 yards and two TDs from Scott Chandler.
The Chiefs (0-1) were led by Matt Cassel, who completed 22-of-36 passes for 119 yards with one touchdown and one interception.
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