The newly acquired Gillaspie homered off Collin Balester in the sixth inning, helping the White Sox beat Texas 8-4 Wednesday and drop the Rangers to 0-5 in spring training.
Obtained Friday from San Francisco for minor league pitcher Jeff Soptic, Gillaspie had four RBIs Tuesday against the Rangers.
"He's not waiting around," said White Sox manager Robin Ventura, a former left-handed-hitting third baseman who likes how Gillaspie sprays the ball to all fields. "He's an aggressive kid, and a tough-minded kid, too."
The 25-year-old Gillaspie spent parts of three seasons with the Giants, hitting .205 with a home run and four RBIs in 29 games and 44 at-bats. San Francisco selected Gillaspie with the 37th overall pick in the 2008 amateur draft from Wichita State. He made his major league debut that Sept. 9.
"I'm just thankful for the opportunity," he said.
Texas manager Ron Washington isn't worried about his team's poor spring training record.
'If we're (winless) after March 31 I'd be having heart attacks or something," he said. "We're putting guys out there. Some are throwing good innings, some aren't. I'm not looking back at no 0-5 start in spring training, that's for certain."
Paul Konerko hit a two-run homer against left-hander Robbie Ross, and 24-year-old right-hander Simon Castro allowed one hit in three scoreless innings for the win. Chicago (3-0-2) is unbeaten through its first five exhibition games for the first time since moving spring training from Florida to Arizona for 1998.
Alexi Ogando, back in the Texas rotation this year after spending 2012 in the bullpen, was the loser. He allowed a pair of unearned runs and three hits in two innings.
Ogando was an All-Star and 13-game winner as a starter in 2011.
"It's going to get better from now on," he said.
Castro, who struck out three and walked none, was acquired after the 2011 season in the trade that sent outfielder Carlos Quentin to San Diego. The 6-foot-5 right-hander who was a combined 7-5 with a 3.85 ERA at Double-A and Triple-A last season. He expects to start the season in the minor leagues.
"This year he has that maturity, more command and that confidence from being another year into it," Ventura said.
Ross, a candidate to be the Rangers' fifth starter, pitched 2 2/3 scoreless innings before Konerko homered. ... White Sox 3B Jeff Keppinger will be limited to designated hitter duty until his still right shoulder clears up, Ventura said. ... The Rangers' Craig Gentry, competing with Leonys Martin for time in CF, was scratched from the lineup with a tight hamstring ... Lance Berkman, who has been bothered by a mild right calf strain, is to make his Rangers spring training debut Thursday.