With Jordan Danks on second base, Gordon Beckham reached when Seattle shortstop Chris Taylor booted his grounder. Danks advanced to third and scored when Gillespie, who entered as a pinch hitter in the eighth, hit a hard single to right off Fernando Rodney (1-5).
The loss ended the Mariners’ four-game winning streak and the White Sox snapped their four-game losing streak.
Former Mariner Hector Noesi worked 7 1/3 innings for the White Sox, allowing one unearned run and five hits with four strikeouts and a walk. Eric Surkamp (1-0) got the last two outs of the ninth for the win and Jake Petricka worked the 10th to pick up his eighth save.