Matt Moore (11-11) set down the first 13 Chicago batters, eventually allowing one hit over 5 1/3 shutout frames. He issued two walks and struck out four.
Tampa Bay retained a slight chance for a post-season appearance, staying within three games of the Oakland Athletics for a wild-card spot with four contests remaining.
Chris Sale (17-8) was tagged for five runs on seven hits, lasting just 3 1/2 innings for second-place Chicago, which fell two games behind American League Central-leading Detroit.
The Tigers beat Minnesota Saturday.
Orlando Hudson supplied an eighth-inning grand slam for the Chisox.
Celebrity Families of 2014 [PHOTOS]