The Guardians opened their series against the Red Sox with a 4-1 victory at Progressive Field.
Ben Lively started the game and struck out seven batters while allowing one run over six and a third innings.
Scott Barlow earned the win after pitching two-thirds of a scoreless inning of relief.
Emmanuel Clase secured his seventh save of the season after striking out three batters in the top of the ninth.
Jose Ramirez went one for four at the plate with a solo homer for his fourth long ball of the year.
Cleveland improved to 17-and-6.