He showed why Saturday.
"Every time he toes the rubber it's a win," reliever Cody Allen said.
Michael Brantley also connected and had three hits for Cleveland, which won at Yankee Stadium for the first time in eight games and improved to 58-59. Ramirez hit a two-run drive in the second inning.
Derek Jeter had an infield single in the sixth inning to pass Honus Wagner for sixth on the career list with No. 3,431. But New York was 0 for 9 with six strikeouts with runners in scoring position in losing for just the second time in eight games.
"I try not to think about it but today, Honus Wagner, he's the last one on the list that has played short at all -- so that one hits home a little bit," Jeter said. "But anytime you're passing guys that have had the careers that they've had, it's kind of overwhelming."
Kluber (13-6) did not allow a hit until Jacoby Ellsbury doubled with one out in the fourth and struck out 10. The right-hander has allowed only one earned run in his last 31 1/3 innings over four starts. He has won six straight decisions.
"Just stick with my same approach. Maybe just executing a little better," Kluber said of his recent success.
Brandon McCarthy (4-1) lost for the first time in six starts with New York. He received a scare in the third when he took a liner off his right foot but he continued for 6 1/3 innings, yielding two runs and seven hits. McCarthy was hit in the head by a liner in 2012 and looked briefly shaken this time.
"I don't think about it," McCarthy said. "It's one of the things when I was coming back that I had to accept the reality that things can come back at you -- you still have to play."
Yankees manager Joe Girardi said x-rays of McCarthy's foot were negative.
Indians: Left fielder David Murphy was lifted after the fifth inning with soreness in the right side. He said his side has been bothering him the last week but got worse Saturday. He will have an MRI. ... Right fielder Nick Swisher was lifted for the eighth inning because of his troublesome right knee.
Yankees: Catcher Brian McCann was placed on the seven-day concussion list. He was hit in the facemask by a foul ball Friday night in the third inning and was feeling foggy when Girardi pulled him for a pinch hitter in the sixth. ... First baseman Mark Teixeira missed a third straight game with an injured pinkie. He said it was too sore to play.
Indians: Carlos Carrasco (3-4) will make his first start since April 25 for Cleveland, taking Danny Salazar's spot. Salazar was demoted to the minors last week. Carrasco was 0-3 with a 6.95 in four starts before being relegated to the bullpen. He has a 2.30 ERA in 26 appearances.
Yankees: Hiroki Kuroda (7-7) is 14-4 with a 2.48 ERA in 24 day games since joining New York in 2012.
SLEEPING ON THE JOB
Indians manager Terry Francona slept on the couch in the visiting manager's office after Friday night's 10-6 loss that took nearly four hours. "I was out cold, man," he said.
Kluber has seven games with at least 10 strikeouts this season, the most by and Indians pitcher since Dennis Eckersley did it eight times in 1976.
McCarthy has walked three or fewer batters in each of his last 105 starts dating to 2009, the longest active streak in the majors.
The fan who caught Ramirez's homer asked for two autographed balls from Jason Giambi, a former Yankee. The Indians said they made the deal.