The Red Sox took over sole possession of the American League East, a half-game ahead of the Yankees, for the first time this season.
Red Sox catcher Sandy Leon had two hits and two RBIs, while left fielder Chris Young had three hits.
Royals third baseman Mike Moustakas gave the Royals a 1-0 lead off Sale in the second inning with his 19th home run this season, and the 100th of his career.