The right-hander ends May as one of the top pitchers in the American League.
Kluber struck out 12 in 7 1-3 innings to continue his dominant pitching in May and the Indians beat the Colorado Rockies 5-2 on Friday night.
"It's fun to write his name in the lineup every five days," Indians manager Terry Francona said. "He continues to get better and better. He's got power, movement and command. He's pretty good."
Kluber (6-3) has been a lot better than pretty good. Other than giving up a two-run homer in the fourth inning to Carlos Gonzalez, he was in complete control of the highest-scoring offense in the NL. He recorded his third double-figure strikeout game this season and ends the month with a 4-0 record and a 2.09 ERA in six starts.
Kluber, who struck out a career-high 13 on May 4 against the Chicago White Sox, finished the month with 60 strikeouts in 43 innings. The right-hander allowed five hits with one walk and was given a standing ovation by the crowd of 25,066 when he was pulled after retiring the first batter in the eighth.
"To do it against that lineup tonight -- that's a very difficult lineup to strike out," Francona said. "That's as much, or more impressive as anything, to do it against that team."
Kluber, who rarely shows any emotion when he's on the mound, downplayed his accomplishments and says he wasn't aware that he leads the AL with 95 strikeouts.
"I had no idea, honestly," he said. "I keep saying when you guys ask me that strikeouts are a by-product of making good pitches. I'm not going out there trying to strike guys out."
Kluber was given several ovations as his strikeout totals rose, but he remained focused on the task at hand.
"I'm kind of locked in when I'm out there," he said. "I don't really notice."
Asdrubal Cabrera's two-run homer broke a fifth-inning tie. The Indians snapped a four-game losing streak while the Rockies fell to 2-5 on their nine-game trip.
Colorado didn't have a hit through three innings, but Corey Dickerson led off the fourth with a double and Gonzalez homered to right-center on an 0-1 pitch with one out.
"It was a changeup, belt high down the middle, it wasn't a good pitch," Kluber said.
Rockies manager Walt Weiss, who was ejected in the sixth inning, was impressed.
"That nasty breaking ball, and we knew he did coming in, but he commanded it and it was a good one," Weiss said. "It was hard and late and he's on a good run. And he threw well again tonight."
Cleveland chased Juan Nicasio (5-3) with a four-run fifth. Michael Bourn's single tied the game before Cabrera's homer put Cleveland ahead. Lonnie Chisenhall, who drove in two runs, added an RBI double.
Kluber struck out the side in the third. He took control after Gonzalez's homer in the fourth. Seven of the next nine outs were strikeouts and he got Charlie Culberson to bounce into a double play to end the seventh.
Cody Allen pitched a perfect ninth for his second save.
Gonzalez returned to the lineup after not starting Wednesday because of a sore right calf. He fouled a pitch off his leg Tuesday and left the game, and was limited to pinch-hitting duties Wednesday. His home run snapped an 0-for-11 slump, but Colorado has 16 runs in the first seven games of the trip and is 5 for 51 with runners in scoring position.
The Rockies' frustration boiled over in the sixth when Michael Cuddyer was called out on strikes by plate umpire John Tumpane. Cuddyer angrily argued the call before being pulled away. Weiss continued the argument and was ejected for the first time in his managerial career.
Michael Brantley extended his hitting streak to 15 games with a fifth-inning double and has hit in 19 consecutive home games, a Progressive Field record.
Jason Kipnis' second-inning single snapped an 0-for-15 slump. He returned Wednesday after missing 25 games with a strained right oblique.
Rockies 3B Nolan Arenado (broken finger) visited doctors at the Cleveland Clinic, who confirmed the diagnosis of Colorado team doctors that he won't need surgery. The plan is to let the finger heal on its own and there's no timetable for his return. ... Indians 3B/C Carlos Santana (concussion) said he's feeling better, but doesn't know when he'll resume physical activities. He was placed on the 7-day DL Tuesday. ... Cleveland RHP Zach McAllister (sore back) threw a simulated game Friday and is scheduled to throw on the side Sunday. ... Rockies LHP Franklin Morales faces RHP Trevor Bauer on Saturday.