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2/27/2013 5:56 P.M. ET

Castro sharp, Konerko goes deep in White Sox win

Right-hander allows one hit over three innings; first baseman hits first homer

GLENDALE, Ariz. -- The White Sox 8-4 victory over the Rangers on Wednesday at Camelback Ranch improved the South Siders' record to 3-0-2 at the outset of the 2013 Cactus League season.

Meanwhile, the Rangers slipped to 0-5. Those records mean almost nothing in regard to the teams' respective standing in the upcoming 2013 regular season, but the White Sox certainly aren't going to look away from a positive start.

Back at SoxFest, White Sox general manager Rick Hahn talked about highly-touted pitching prospects Nestor Molina and Simon Castro, their rough seasons in 2012 and their need to rebuild in the 2013 season. If the past two games against Texas are any indication, they both are on the right track.

Molina threw two scoreless innings in Tuesday's victory in Surprise, and Castro came back with three scoreless innings during Wednesday's victory. Castro struck out three and allowed one hit while issuing one walk, in an effort to bounce back from a decent if not spectacular 2012 season, during which the right-hander was bothered by a strained right forearm.

"We're just trying to take it day by day," Castro said. "I'm not focusing on what happened last year. I'm just focusing on what's going to happen this year. I'm just going to focus on an everyday basis now."

Texas pitcher Robbie Ross was one out away from having a second impressive outing in his bid to win a spot in the Rangers' rotation. After Alexi Ogando allowed two runs in two innings, Ross held the White Sox scoreless in the third and fourth. But he couldn't do that in the fifth.

He got one out on a fly to center and then picked off Alex Rios at first base after Rios reached on a single. But Ross hit Adam Dunn with a pitch and then gave up a two-run home run to Paul Konerko. Ross had Konerko at 3-2, but couldn't put him away.

Instead, Konerko hit a high fly ball to left that landed just on top of the left-field wall for a two-run home run. Dayan Vicideo singled to left, but Ross got Josh Phegley on a grounder to third. Ross has a 3.60 ERA in his first two Cactus League games and opponents are hitting .250 against him.

"Just a 3-2 count, a fastball and Konerko got it," Ross said. "I felt good. Everything was going right until he got a hold of it."

After the Rangers rallied for three in the sixth -- driven in by Nelson Cruz, Jeff Baker and Brandon Allen -- against Jeff Gray, who struck out the side, Conor Gillaspie lined a two-run homer to right to raise the White Sox lead back to three in the sixth. Gillaspie has a single, triple and homer in his last two games for the White Sox.

Pedro Borbon added the Rangers' final run with an RBI groundout in the eighth.

White Sox up next: Scott Snodgress worked in relief during his first Cactus League outing but he will be getting the start Thursday against the Brewers. This start by the southpaw marks the last prospect to take the mound in this capacity, with the White Sox going back to the regular rotation on Friday with Chris Sale. Dylan Axelrod, who opened Cactus League action with three scoreless innings, will work in relief. Nate Jones, Addison Reed and Matt Lindstrom also are scheduled. First pitch Thursday is at 2:05 p.m. CT.

Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.