Rangers starter Rich Harden (3-1) hung around long enough to get the victory, allowing four runs on seven hits. He struck out one and allowed three walks.
Buehrle (3-6) couldn't hold on to an early 4-0 lead. Buehrle was tagged for four runs on four hits in the sixth inning.
"He's going to work fast. He's going to throw his changeup down in the zone and try to get you to roll over, but we were able to get to him a little bit in the first inning and make him throw a lot of pitches," Kinsler said. "I think that might have affected him later in the game when he was getting up to about the 100 pitch count. It kind of tired him out a little bit."
Rangers reliever Frank Francisco struck out the side in order in the seventh and Darren Oliver struck out two for a perfect eighth inning. But closer Neftali Feliz loaded the bases in the ninth with one out before getting Alexei Ramirez to popout and Omar Vizquel to fly to center for his 14th save in 16 opportunities.
Justin Smoak also had a pinch-hit RBI single and a solo home run for Texas.
Carlos Quentin homered for Chicago.
With one out in the sixth inning and leading 4-2, Buehrle gave up four consecutive singles. With the bases loaded, Gentry, who was recalled from Triple-A Oklahoma City on Sunday, lined a single up the middle to score Joaquin Arias and Murphy to end Buehrle's outing.
"We got together and talked about things we needed to do when we got guys in scoring position, things like that. It seemed to work out a little better tonight," Hamilton said.
Michael Young followed with a sacrifice fly off reliever Sergio Santos to put the Rangers ahead and Kinsler capped off a five-run inning with a two-run double down the left-field line to give the Rangers a 7-4 lead.
"We score four runs in the beginning of the game, with Buehrle on the mound, you're a little excited about the game," White Sox manager Ozzie Guillen said. "Then all of a sudden, everything was turned around. We could have scored some more, we left opportunities out there. We came short, and obviously our pitching wasn't that good."
Buehrle made his first start since being ejected by umpire Joe West for flipping his glove after being called for his second balk of the game in the second inning of Wednesday's win at Cleveland. He allowed six runs on a season-high 12 hits.
Although he did not give up a run in the first inning he threw 37 pitches.
"This is a game of being bad from the get go and pitching out of some jams early. Obviously when you're falling behind the count and getting guys on base and pitching out of the first couple of inning it's going to catch up for you," Buehrle said. "I felt good, I was just all over the place and couldn't find the strike zone."
In the second inning, Harden gave up a leadoff home run to Quentin. He then allowed three consecutive singles to Ramirez, Vizquel and Beckham. Ramirez scored on Beckham's single and Vizquel scored on A.J. Pierzynski's groundout to give the White Sox a 4-0 lead.
Rangers RHP Brandon McCarthy threw a bullpen session on Tuesday in Oklahoma City. If the bullpen session went well McCarthy could be activated off the minor league disabled list and be used as a reliever for Triple-A Oklahoma by the end of the week. ... Before the game, the White Sox placed Mark Teahen on the 15-day DL with a fractured right middle finger. INF Brent Lillibridge was called up from Triple-A Charlotte took his spot on the roster.