The Indians scored the go-ahead run in the seventh inning and then tacked on three more in the ninth to down the White Sox 4-0 last night in Chicago.
Tribe starter Corey Kluber struck out eleven batters over seven innings to win his career best 20th game of the season.
Kluber becomes the first Cleveland pitcher to win 20 games in a season since 2008 when Cliff Lee went 22-3.
The Indians play the second of three games at the White Sox tonight.
Cleveland has already clinched the AL Central with an 88-and-68 record.
Trevor Bauer starts for the Indians opposite Chicago's James Shields.