Travis Shaw hit a two-run home run in the first inning to give the Brewers an early 2-0 lead.

Jose Ramirez and Francisco Lindor each hit solo home runs for the Indians, who have lost four of five but remain in first place in the downtrodden American League Central.

Ramirez, the reigning American League Player of the Week, homered to center in the third inning to cut the Brewers' lead to 2-1. It was his 10th home run of the season.

In addition to clubbing his first career home run -- a solo shot to lead off the third inning -- Suter (2-2) also pitched 4 2/3 innings after Milwaukee starter Wade Miley had to leave the game in the first inning with a side injury.

Miley faced four batters in the first before motioning to the dugout to send out the trainer after throwing a pitch to Michael Brantley. Miley, who was making only his second start of the season for the Brewers, left the game with what the team called a right oblique strain.

Suter replaced Miley and got out of jam by striking out Edwin Encarnacion with runners on second and third.

Suter went deep leading off the bottom of the third to boost the lead to 3-1. Lindor's ninth homer, leading off the fifth inning, produced the game's final run.

Kluber (5-2) surrendered three runs on five hits in six innings, with four strikeouts and one walk. He had won his previous five starts.

Suter surrendered two runs on five hits and a walk while striking out five.

The Brewers loaded the bases with one out in the eighth inning, but Cleveland reliever Zach McAllister struck out Manny Pina to end the threat and keep the Indians within one heading into the ninth inning.

Milwaukee closer Josh Hader worked two scoreless innings, and he retired the Indians in order in the ninth for his fifth save.

--Field Level Media