The Indians did all of their scoring in the first two innings as they bombarded the Royals, 12-0, in Cleveland.
The Tribe put together a nine-run second, consisting of a Yan Gomes grand slam, a three-run homer by Carlos Santana, and a two-run shot from Francisco Lindor.
Carlos Carrasco hurled seven shutout innings for the win.
Cleveland secured the shutout sweep at home and leads the AL Central by six-and-a-half games.
Royals starter Eric Skoglund gave up seven hits and seven runs while recording just four outs to take the loss.
The Royals haven't scored a run in the past 34 innings, a franchise record. They're nine games back in the division race.