Ben Zobrist added a two-run homer, Desmond Jennings hit a solo shot and James Loney supplied two RBI as the Rays bounced back with 19 hits after dropping the first two contests in their four-game road series.
Matt Moore (5-0) stymied the White Sox on one run over six innings, yielding three hits while striking out nine.
Chicago starter Gavin Floyd (0-4) yielded two runs on two hits before exiting with a right elbow flexor muscle strain after 2 2/3 innings.
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