Spiller also hauled in three passes for 47 yards as Buffalo (1-1) rebounded from a one-sided loss to the New York Jets in last week's season opener.
Ryan Fitzpatrick completed 10-for-19 attempts for 178 yards and two touchdowns in the win.
The Chiefs (0-2), meanwhile, have surrendered 75 points in their first two games, both losses.
Matt Cassel racked up 301 passing yards on 23-for-42 efficiency but yielded an interception and lost a fumble.
Dwayne Bowe led Kansas City receivers with had eight grabs for 102 yards and two scores.
Swim Week Miami Beach 2014 [PHOTOS]