The Indians defeated the Yankees 4-0.
Bauer got Yankees superstar Aaron Judge to strikeout three times.
Jay Bruce drove in three of the Indians four runs.
He smacked a home run to right field in the fourth inning, Bruce also hit a sacrifice fly in the fifth inning to make it a 4-0 game.
Roberto Perez was the first Cleveland batter to put the Indians on the board after grounding into a double play with the bases loaded.
Sonny Gray got the start for the Yankees, he only pitched 3.1 innings.
Game two is set for 5 p.m. on Oct. 6.
This is the fourth time the Yankees and Indians have played against each other in the playoffs.
The last time the two teams have played each other in the postseason was in 2007, Cleveland won the series 3-1.