Nance, who played his college football at Arizona State, produced a 2-yard touchdown run in the third quarter and then scored from a yard out in the fourth to finish off an 18-play, 80-yard drive that took 9:23 off the clock.
The Falcons got field goals of 30 yards from Matt Bryant and 37 yards from Steven Hauschka.
Kansas City's only touchdown came with 18 seconds remaining in the game on a 1-yard run by Tyler Palko.
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