Clevinger allowed one hit over 5 2/3 innings as the Indians blanked the Kansas City Royals 1-0 on Sunday. That was the only hit the Indians' staff allowed as four relievers combined to strike out six after Clevinger exited.
Salvador Perez's fourth-inning double was the lone Kansas City hit.
Clevinger (1-0) struck out five and walked four in 5 2/3 innings before manager Terry Francona went to his bullpen to protect the one-run lead.
"I thought his stuff was good," Francona said. "You could tell he made a few adjustments in Triple-A with his delivery. I wouldn't say he was wild, but he had the walks and got into some deep counts that got the pitch count up.
"His changeup was good, his breaking ball was good. It gets you excited because we've seen not only did he get them out, but for the future you've seen he's made a couple of adjustments and has got a chance to go deep into a game."
Clevinger was recalled from Triple-A Columbus to replace the injured Kluber in the rotation.
"I just commanded the bottom half of the zone," Clevinger said. "It was controlled intensity. I wasn't trying to throw 96-96 every pitch. It was finding my rhythm, finding the lower half of the zone and then trying to repeat that.
"It's awesome to be back with these guys. I missed these guys, missed the defense and the bats."
Left-hander Andrew Miller pitched a flawless eighth. He has allowed no runs and eight hits in 15 2/3 innings this season.
"The last few I've kind of scuffled a little bit with my delivery," Allen said. "Hopefully, I can get a little more consistent as we move forward. I haven't really commanded the ball at all.
"We were to pull it out today, it was a good win, a huge series win. I had no idea it was a no-hitter."
Allen retired pinch hitter Brandon Moss on a fly ball to center to end the game with two runners on base.
"He made a great pitch," Moss said. "He has that ability, that's why he's the closer. He has plus-plus stuff and the ability to locate pitches well when he needs to."
"I've got to catch that ball," Duffy said. "I just thought it was hit harder than it was. If it was hit harder, I would have caught it, which is kind of ironic. It was like a changeup. There's nothing more I could have done. I did everything that I tried to do.
"I just strive for better. I've got to be better. As soon as it got past me I knew I should have had it. I'm a better athlete than that."
Duffy (2-3) took the loss, allowing one run on six hits over 6 23 innings.
The Indians got a runner into scoring position in two of the first three innings but could not get them home.
Santana led off the game with a double and Francisco Lindor bunted him to third, but Santana went no farther.
Santana opened the third with a single and went to second when Perez made a spectacular twirl and throw from behind the plate to get Michael Brantley out. Edwin Encarnacion's groundout stranded Santana.
Clevinger held the Royals hitless until one out in the fourth. After Eric Hosmer drew his second walk, Perez drilled a double to left. Third base coach Mike Jirschele stopped Hosmer at third.
Clevinger then applied the brakes by striking out Soler looking and Jorge Bonifacio swinging to maroon Hosmer.
NOTES: The Indians optioned RHP Joe Colon to Triple-A Columbus. He was recalled Wednesday but did not appear in a game. Colon was optioned so Sunday starter Mike Clevinger could be added to the roster. ... The Royals wore 1942 Kansas City Monarchs replica uniforms and the Indians 1946 Cleveland Buckeyes unis in a salute to the Negro Leagues. ... Royals C Salvador Perez was back in the starting lineup, although he left Saturday's game with a bruised left forearm after being hit by a foul ball. ... Indians RHP Trevor Bauer will start the Monday series opener at Toronto. The Blue Jays will go with RHP Marcus Stroman. ... The Royals will open a four-game series Monday at Tampa Bay with RHP Nate Karns the probable starter. The Rays will counter with LHP Blake Snell.