Robin Ventura has one luxury while he tries to find the right combination to snap the White Sox out of their offensive funk.

Injuries and the addition of Conor Gillaspie give the Sox enough left-handed hitters to combat tough right-handed pitchers like the Rays' Jeremy Hellickson.

Starting with Alejandro De Aza's double in the first and ending with Adam Dunn's two-run home run in the sixth, the Sox's left-handed hitters provided enough production to help beat Hellickson and the Rays 5-2 on Thursday night.

This marked the first time the Sox had scored more than three runs since April 17 in Toronto. They accomplished this against Hellickson, who had allowed only five runs in his previous 19 innings and had limited right-handed batters to a .111 average.

"These guys are putting out everything they have, every single day," said Chris Sale, who overcame four walks to pitch seven innings of four-hit ball. "I know the results haven't been great, but don't think for a second it's because of a lack of focus or a lack of effort. These guys are grinding it out. On my days off when I'm not pitching and actually get to watch a little bit of it, I see these guys working hard, hitting flips in the cage and watching video.

"It was awesome to see them come out (in the) first. I'm kind of kicking myself for giving up one in the first, and next thing, double, double, and we got three runs in the first. And Dunn came up huge in the sixth and gave us a cushion to play with. It was an all-around great game."

De Aza and Jeff Keppinger fueled a three-run first with consecutive doubles. And Keppinger beat the tag of catcher Jose Lobaton to score the Sox's second run with a clever slide.

This was the type of aggressive baseball the Sox hadn't displayed throughout most of the first 31/2 weeks of the season.