Royals starter Danny Duffy lasted only 3 2/3 innings, lifted after allowing one run on five hits and four walks.
But Smith (2-1) then stepped up and tamed the Mariners on one hit while striking out eight.
Greg Holland finished up with a scoreless ninth for his 37th save as the Royals took the first of a four-game series.
Mike Moustakas and Emilio Bonifacio each provided an RBI for the winners.
Seattle ace Felix Hernandez (12-9) fell in a fourth straight start, yielding three runs on six hits over 6 2/3 innings.
Brad Miller drove in the M's only run.