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CLEVELAND -- Asdrubal Cabrera has been carrying the Cleveland Indians all season.

He did it again Tuesday with a leadoff home run in the fourth that broke a tie game, and the Indians defeated the Chicago White Sox 4-3 in the first game of a day-night doubleheader.

"He's had an outstanding season," Indians manager Manny Acta said of his switch-hitting shortstop. "He's hit for power and driven in runs. His numbers have been great."

Cabrera's home run put Cleveland ahead and was his team-leading 24th of the season. He also leads the Indians with 87 RBIs, eclipsing his previous career high of 68 in 2009.

"I'm really happy with what I've done, but I haven't thought too much about it," he said. "I think we've had a good season, and it's not over yet."

Cabrera has been a constant in a season that has seen several teammates miss significant time with injuries, including Shin-Soo Choo, Grady Sizemore, Travis Hafner and Michael Brantley.

But even he can't escape the injury bug.

Cabrera said he hurt his back during his last at-bat in the eighth inning attempting to bunt for a hit.

"It hurt a lot when it happened, but it feels better now," said Cabrera, who hopes to be back in the lineup in a couple of days.

Cabrera, who entered Saturday's game against Minnesota in an 0-for-20 slump, has eight hits in his last 13 at-bats. He has homered in back-to-back games.

"He's struggled a little bit in the second half, but he's played well all season," Acta said.

Fausto Carmona (7-15) allowed three runs in six innings and won for the first time since Aug. 17.

Hafner and Kosuke Fukudome also homered off Gavin Floyd (12-12), who hasn't won since Aug. 29. Chicago has lost eight of its last nine games.

"I didn't think they were terrible pitches, they just got the right part of the bat on the ball," Floyd said of the home runs. "They could have just as easily been fly balls, but today they weren't."

The teams, who were eliminated from the AL Central race last week when Detroit clinched the division, are battling for second place. The Indians lead the White Sox by 2½ games.

Hafner's two-run homer in the first gave Cleveland the lead, but Chicago tied the game in the second on Adam Dunn's RBI double and Alejandro De Aza's run-scoring single.

Fukudome homered with one out in the fifth.

Carmona struck out three and walked two. Relievers Joe Smith, Vinnie Pestano and Chris Perez, who recorded his 35th save, blanked Chicago over the final three innings.

Chicago's first four hitters reached against Carmona in the second. Singles by A.J. Pierzynski and Alex Rios started the inning. Dunn, batting .165 when the game began, slapped a double down the third base line that scored Pierzynski. De Aza's single to right tied the game.

De Aza added an RBI groundout in the sixth.

Floyd gave up four runs and seven hits in 6 2/3 innings. He struck out seven and didn't walk a batter.

Game notes

The game was the makeup of a July 23 rainout at Progressive Field. ... White Sox manager Ozzie Guillen says LHP Mark Buehrle will start Wednesday night. Buehrle (11-9, 3.74 ERA) has sore biceps after being hit with a ball in his last start. RHP Ubaldo Jimenez (4-2, 4.56) will start for the Indians. ... Guillen played most of his regulars in Tuesday's first game. ... The White Sox are 9-6 against the Indians with three games to play in the season series. ... Indians 3B Jack Hannahan was a defensive replacement in the eighth inning, his first appearance since straining his left calf Sept. 4. ... C Lou Marson struck out in all three at-bats. ... The Indians are playing nine games in seven days on their final homestand of the season. Cleveland played a makeup game with Seattle on Monday and will play another day-night doubleheader against Minnesota on Saturday. ... The Indians recalled RHP Corey Kluber from Triple-A Columbus.