Matt Joyce socked a two-run homer and scored three runs while Jose Lobaton added a solo shot for the Rays, who scored five times over the final two innings to break open a close contest.
Reigning Cy Young Award winner David Price (1-2) earned his first victory of the season in his sixth start, striking out nine over six full innings. The left-handed ace yielded six hits and a pair of walks.
The victory gave the Rays a split of their four-game road series.
Chisox reliever Nate Jones (0-2) absorbed the loss in relief of Dylan Axelrod, who surrendered three runs on four hits over six frames.
Paul Konerko socked a two-run homer for Chicago.
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