Corey Kluber struck out 10 over six and two thirds innings as the Indians beat the Royals 3-1 at Progressive Field.
Kluber allowed just two hits and one run en route to his 18th win of the season.
Greg Allen, Edwin Encarnacion and Jason Kipnis drove in runs.
The Indians are north of the border tonight as they battle the Blue Jays in Toronto.
It's the first of a four-game series, with Shane Bieber starting for Cleveland and Sam Gaviglio for the Jays.
The Tribe now leads the Twins by 16 games atop the AL Central.