Jeff Samardzija wound up in the win column for the first time with the Chicago White Sox, helped by a couple of big swings Jose Abreu took against Corey Kluber.

Samardzija threw six shutout innings as the White Sox trounced the reigning AL Cy Young Award winner and the Cleveland Indians 6-0 on Wednesday.

Samardzija (1-1) had been winless in his first three starts for the White Sox. The 30-year-old righty from nearby Merrillville, Indiana, allowed six hits, walked two and struck out three.

"You get new teammates and you want to make sure you prove your worth to them," said Samardzija, acquired in a trade with Oakland in December.

"They gave me an early run, early two runs. That's a big cushion to have and that allowed me to go out and pound the zone with what I thought was subpar stuff," he said.

Abreu homered for the second straight day. He hit a solo shot in the first inning and added a two-run double in the seventh to chase Kluber (0-2).

Kluber gave up a career-high 13 hits and six earned runs in his fourth start of the year. He struck out six, walked one and threw two wild pitches, and was pulled before he got an out in the seventh.

"I made some mistakes and I probably didn't do a good enough job pitching inside to keep them off balance when I did make those mistakes," Kluber said.

Samardzija gave up two singles and a walk to load the bases in the third, but got out of the jam when Brandon Moss filed to right to end the inning.

Samardzija left with the two-run lead after throwing 113 pitches.

"He labored a little bit," White Sox manager Robin Ventura said. "When he needed to make a pitch, he made a pitch. He has some tools to him. . It's nice to him to gut through and get to a point where we could get to the bullpen."

Adam Eaton doubled to open the third, reached third on Melky Cabrera's single and scored on Abreu's double-play grounder to make it 2-0.

Kluber gave up another run in the sixth when his wild pitch let Avisail Garcia score.

Chicago made it 4-0 in the seventh as Cabrera singled home Micah Johnson. Abreu's double to deep left scored Eaton and Cabrera.

"It's a hard way to pitch when we're throwing up zeroes as an offense," Indians manager Terry Francona said. "I think he probably feels like he has to be perfect and that's a hard way to pitch."