Smith's pick-off of rookie quarterback Jeff Tuel came as the Bills were leading 10-3 early in the third quarter, and turned the tide for the Chiefs (9-0), who remained the NFL's lone unbeaten squad.
Tamba Hali's 11-yard fumble recovery for a score in the fourth quarter broke a 13-13 tie.
Tuel finished 18-of-39 through the air for 229 yards with two costly interceptions in his first NFL start for Buffalo (3-6).
He was playing due to injuries to quarterbacks E.J. Manuel and Thad Lewis.
C.J. Spiller ran for 116 yards on 12 carries in his return from a sprained ankle.
Swim Week Miami Beach 2014 [PHOTOS]