Casey Kotchman and Michael Brantley each hit two-run doubles in a five-run third inning, as Cleveland held on and topped Chicago, 8-6, in the opener of a twinbill.
Travis Hafner finished 2-for-4 with a homer and Asdrubal Cabrera also knocked in a run for the Indians, who have won five of their last six.
Zach McAllister (1-0) allowed six hits and four runs -- two earned -- over six innings.
"I thought I was able to make some good pitches when I needed to and I was definitely happy I gave the team some innings," said McAllister.
Alexei Ramirez collected two hits and knocked in three runs for the White Sox, who have lost five of six. Brent Lillibridge and Kosuke Fukudome added an RBI apiece in defeat.
Philip Humber (1-2) didn't make it out of the third inning, charged with nine hits and eight runs with two walks while recording seven outs. The right- hander has given up 20 earned runs in three starts since his April 21 perfect game.
"Obviously my location couldn't have been great," Humber said about his outing. "I just didn't have it."
Chicago closed within 8-4 on a Ramirez double and Fukudome sacrifice fly in the fourth, but caused trouble for Jairo Asencio in the ninth.
A.J. Pierzynski and Alex Rios both walked, and a wild pitch moved both runners into scoring position. Ramirez lined a single to center which scored both and pulled the Sox to 8-6, but Nick Hagadone rescued the Tribe by getting three of the next four batters out to preserve the victory.
After a rain delay of 26 minutes at the outset, Alejandro De Aza began the game with a double and went to third on a throwing error, then scored on a Lillibridge sac fly.
Cleveland responded with three in the home second as Hafner led off with a homer, Brantley hit an RBI single and Kotchman added a run-scoring fielder's choice grounder.
In the third, Gordon Beckham doubled with one out, De Aza singled and Beckham then scored when Tribe catcher Carlos Santana threw wild to second on De Aza's steal attempt.
The Indians exploded in the home third, moving ahead 5-2 on Brantley's one- out, bases-loaded double, then stretching the edge to five when Kotchman followed with a two-run double.
Humber exited after walking Jack Hannahan to re-load the bases, but Jose Quintana walked Jason Kipnis and then forced in another run via a base on balls to Cabrera.
Cleveland has won three in a row over the ChiSox to even the season series...Chicago had taken a truncated two-game series in Ohio on April 9 and 11...Brantley and Kotchman each finished with three RBI...Humber's eight earned runs allowed was his second-most given up this season, after he surrendered nine to Boston in a 10-3 loss on April 26, one start following that memorable 4-0 win at Seattle.