Carmona (8-2) pitched seven-plus innings to help the Indians avoid a three-game sweep with a 5-2 win over the Atlanta Braves on Sunday.
"It was another great performance by Fausto," said manager Eric Wedge, who believes the 23-year-old should be an All-Star. "I do think he deserves to make it. He's earned it."
Casey Blake extended the majors' longest hitting streak of the season to 26 games for Cleveland, which won for only the third time in eight games and remained in first place in the AL Central.
Chipper Jones got his 2,000th hit for the Braves, losers of 10 of their last 15.
"It's a pretty cool number," Jones said. "It's one of the numbers you reach when you've been around a long time. My next goal is to work on the next thousand, but I don't know if I'll play that long."
Jones, 35, got his first hit as a pinch hitter in his first career at bat on Sept. 14, 1993.
Scott Thorman ruined Carmona's bid for his second career shutout by hitting his eighth homer to lead off the eighth inning. Carmona then issued his only two walks and was replaced by Rafael Betancourt.
Willie Harris lined an RBI double into the right-field corner to make it 5-2. It was the first of 18 inherited baserunners to score against Betancourt this season.
The right-hander came back to strike out Edgar Renteria, who went 0-for-4 one day after going 5-for-5 in the Braves' 6-2 win on Saturday. Jason Michaels made a diving catch in left to take a hit away from Chipper Jones and Betancourt struck out Andruw Jones to get out of the inning.
"That was the only breaking ball I threw," Betancourt said of the called strike over the outside corner that ended the threat. "But J-Mike made an awesome play. Just great."
Joe Borowski worked the ninth for his 100th career save. He is 20-for-22 in save chances this year.
Carmona gave up two runs and five hits, striking out five to improve to 6-0 in day games, which leads the majors. He opened the season in Cleveland's rotation only because of an injury to veteran Cliff Lee, but is 8-1 in 11 starts since losing his season debut April 13. That was his 11th straight loss over two seasons and dropped his career record at the time to 1-11.
"He has a bright future. I was really impressed with him," Chipper Jones said.
The Braves failed to get their first road sweep of an AL opponent since taking three games at Boston on June 28-30, 2002. Two Atlanta errors helped the Indians take a 5-0 lead with a four-run sixth against Kyle Davies (3-6).
Victor Martinez singled and went to third on a double by Jhonny Peralta to right-center. Ryan Garko then hit a check-swing bouncer that first baseman Thorman misplayed, allowing both runners to score.
"It was a tough hop," Thorman said. "It really stinks because Kyle pitched well and it was the deciding play of the game. I wish I had it back."
Michaels' two-out RBI single gave Cleveland a 1-0 lead in the fifth.
Chipper Jones' milestone hit was a line-drive single in the second. He needs three doubles to join Hall of Famer Eddie Murray and Chili Davis as the only switch hitters to collect 2,000 hits, 400 doubles and 350 home runs. Jones has 369 career homers, two behind Braves legend Dale Murphy.
Blake's first-inning single to right broke a tie with Ichiro Suzuki of the Seattle Mariners for the longest hitting streak this season. It is the longest streak by a Cleveland player since Sandy Alomar Jr., hit safely in 30 consecutive games in 1997.
- CF Grady Sizemore got a standing ovation after making a diving catch to end the seventh inning, robbing Braves RF Jeff Francoeur of a hit. That came after Michaels' sliding catch took a hit away from McCann.
- Members of the rock group Barenaked Ladies sang the National Anthem and threw out ceremonial first pitches.
- The three-game set in the Braves' first appearance in Cleveland since beating the Indians in the 1995 World Series drew 103,430 fans.