Sale (17-9) allowed three runs and eight hits with seven strikeouts over seven innings, retiring the last seven batters to match his career high in victories in Chicago's fourth straight win.
Cabrera belted a two-run homer in a three-run first inning and Garcia added a three-run shot in the third. Garcia also tripled when Mikie Mahtook misplayed his liner to center in a two-run second.
Rays starter Alex Cobb (1-2) lasted three innings, allowing eight runs and eight hits in the Rays' fifth straight loss.
Tim Anderson added three hits, including a solo homer in the eighth off Chase Whitley, the 204th allowed by Tampa Bay this season.
Ex-White Sox shortstop Alexei Ramirez had a two-run single in the second and Curt Casali led off the fourth with a homer for the Rays, who have scored 11 runs in five games.
