CHICAGO -- After more than a week of losing, the Chicago White Sox needed their star to find the win column again.
"We just came out of a bad moment, a bad stretch," Abreu said through a translator after the game. "I was concentrating since yesterday on this pitcher because I knew it was going to be tough."
Kluber (13-8) lost consecutive starts for the first time this year, allowing three runs and nine hits in 6 1/3 innings with eight strikeouts. He entered Wednesday's contest with a 2.46 ERA.
"He worked hard tonight, but he ended up giving up three runs and one was on a late hit," Indians manager Terry Francona said of his starting pitcher. "He is pretty damn good. If we score five or six we're talking about him cruising."
The Indians had won three straight.
Abreu put Chicago ahead for good in the seventh with his third hit of the game. Eaton doubled with one out off Kluber and advanced on Alexei Ramirez's groundout. Abreu then singled up the middle, driving in Eaton for his AL-high 96th RBI.
"He's amazing, isn't he?" Eaton said of Abreu. "Great player. Rises to the occasion like he has all year."
Eaton was 2 for 4 with one double, one triple and two runs scored.
White Sox starter Hector Noesi (8-9) allowed two runs and six hits in seven innings, improving to 5-2 in eight starts since the All-Star break.
"Hector (Noesi) threw a great game," White Sox manager Robin Ventura said. "He's going up against a tough pitcher. Being able to get us to that point was big."
Javy Guerra pitched a perfect eighth inning, but he allowed Jason Kipnis' one-out single in the ninth and hit Zach Walters with a pitch with two outs. Zach Putman relieved and retired Chris Dickerson on a fly out for his fourth save in five chances.
Michael Bourn's run-scoring single put Cleveland ahead in the third. Chicago went ahead in the bottom half when Abreu hit an RBI single with two outs and scored on a double by Adam Dunn.
Lonnie Chisenhall wrapped a 339-foot homer around the right-field foul pole in the seventh, his 12th home run this season.
Indians: C Yan Gomes is expected to be available Friday when he comes off the seven-day concussion disabled list. Gomes took a foul ball off the mask last week against Minnesota.
White Sox: Manager Robin Ventura dismissed the notion that outfielder Avisail Garcia, who missed more than four months with a torn labrum in his left shoulder, has played hesitantly since returning from the DL and may still be ailing. "I don't think so," Ventura said. "That's just the way he plays outfield."
In his 18th and final MLB season, White Sox first baseman Paul Konerko took some time before Wednesday's game to praise Chicago's Jackie Robinson West All-Stars, who won the Little League World Series national championship over the weekend. "It's cool to see," Konerko said. "Baseball has taken a back seat to a lot of other sports lately -- you've seen a lot more kids playing other things -- so hopefully, at least in Chicago, this maybe pushes a kid to our game instead of something else."
KLUBER TAKES EXCEPTION
After an umpire review in the seventh inning, Kluber was not allowed to throw extra warm-up pitches since the review had concluded. He took exception to the call. "I don't get the whole making up rules as we go," Kluber said after the game. "Every other time I was out there for a replay, I was able to throw a couple of pitches, and all of sudden I'm told I'm only able to throw pitches while they're reviewing the play. So the umpire is making up stuff as we're going. The system needs to be looked at."