With an 83-76 record, the Guardians now lead the Chicago White Sox (82-77), who clinched their Postseason spot earlier in the day, for the AL Central title.
Angel Martinez brought in the game's only run when he launched a solo home run in the top of the first inning. David Fry (1-for-4) and Jose Ramirez (2-for-4) had the other three hits for the Guardians.
Five of their pitchers combined for a two-hit shutout, giving up just four walks with 12 strikeouts. It marked just the sixth shutout for the team this season.
After winning the Central in back-to-back seasons, the Guardians are looking to make the World Series for the first time since 2016. The Guardians haven't won a title since the name change, and the last time the franchise as a whole won it all was in 1948.
Their 78 seasons without a ring is the longest active drought in Major League Baseball. The Milwaukee Brewers, who currently hold the best record in baseball at 99-59, and San Diego Padres, who are looking to clinch a Wild Card spot, are behind the Guardians with a 58-year drought - never having won a ring in the first place.