Smith went 21-of-36 through the air and set up a go-ahead field goal by Ryan Succop early in the fourth quarter as the Chiefs improved to 2-0, already matching their 2-14 mark from last year in the win column.
The Cowboys (1-1) got 141 receiving yards and a score on nine grabs from Dez Bryant, but it wasn't enough to follow up last week's season-opening victory over the New York Giants with another triumph.
Tony Romo tossed for 298 yards on 30-of-42 efficiency in the loss.
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