''Klubes has pitched to the point where, heck yeah, you better play with confidence,'' manager Terry Francona said. ''He's one of the best pitchers in the league.''
Kluber (12-6) continued his dominant stretch by allowing one run over 7 1-3 innings in Monday night's 7-1 victory over the Cincinnati Reds.
Kluber, who hasn't lost since June 30, held the Reds to six hits, struck out seven and walked two in winning his fifth straight decision.
''I started out not so great with my command, but I was able to reel it in and had better command in the middle of the game,'' he said.
The only bad news came in the eighth when Kluber's 17-inning scoreless streak ended on Brayan Pena's RBI double off reliever Nick Hagadone. That also ended the right-hander's stretch of not allowing an earned run at 25 innings.
Francona pulled Kluber, who received a standing ovation from the 18,696 fans. The crowd groaned when Pena's hit pushed a run across the plate.
''Every starter wants to go deep into the game, but in that situation when it was still close, and my pitch count was up,'' Kluber said. ''I understand.''
The series between the intrastate rivals features teams trying to remain in playoff contention. The win lifted the Indians (57-55) two games over .500 for the first time since July 22. The Reds are 5-12 since the All-Star break and fell to .500 (56-56).
Kluber stopped Seattle on a three-hitter Wednesday and took a perfect game into the seventh inning against Kansas City on July 24 in his previous start, with the Royals scoring an unearned run in the eighth.
Kluber's only loss in his brilliant stretch came in a 1-0 defeat to the Los Angeles Dodgers.
''You go through periods where you have things working and even when you're not at your best, you're still good,'' Francona said. ''That's kind of where Klubes is getting.''
Michael Brantley added an RBI groundout in the first inning and a run-scoring single in the fifth.
John Axford pitched the final 1 2-3 innings for his 10th save.
Cincinnati manager Bryan Price praised Kluber's performance. ''As advertised,'' Price said. ''I know he's a tremendous pitcher, we all knew that coming in. He did the things that we knew about. He's very good.''
Center fielder Michael Bourn will begin a minor league rehab assignment at Double-A Akron on Tuesday. He hasn't played since July 5 because of a recurring left hamstring injury.
Reds: Second baseman Brandon Phillips is traveling with the team as he continues to rehab from a torn ligament in his left thumb. Price said Phillips, who hasn't played since July 9, still can't swing a bat.
Indians: Designated hitter Nick Swisher is optimistic his strained right wrist won't sideline him for more than a couple of days. ''I've been through stuff like this before,'' he said. ''It's just a little tight.'' He injured the wrist in his last at-bat Sunday against Texas' Yu Darvish.
Reds: All-Star right-hander Johnny Cueto (12-6) will start Tuesday. He leads the NL in innings pitched (162 2-3) and opponents' batting average (.183) and is second in ERA (2.05) and strikeouts (186). Cueto is 3-0 in five career starts against Cleveland.
Indians: Right-hander Josh Tomlin (5-7) will be called up from Triple-A Columbus to start Tuesday. He was sent to the minors on July 26. Tomlin hasn't won since pitching a one-hitter on June 28. He's 1-1 in three career appearances against Cincinnati.