Michael Young and Teixeira hit back-to-back homers off Buehrle to lead the Rangers to a 10-3 victory on Friday night.
Buehrle has lost his last four starts and during the span he has given up 27 runs in 21 1/3 innings for the White Sox, who have lost eight of their last 10 games and are 1-6 since the All-Star break.
"If you expand the zone and swing at his pitch you're not going to have any success. We did a good job of hitting pitches we could handle and we got to him," said Teixeira, who broke out of a 2-for-20 slump with the home run.
Kevin Mench hit a three-run homer in the eighth for the Rangers and Brad Wilkerson added a solo shot in the ninth.
With the loss, the White Sox trail the first-place Detroit Tigers by 6 1/2 games in the AL Central, but they maintained a 2 1/2-game lead over the New York Yankees in the wild card.
"I told them to just continue to play. We know we're going to win a lot of games, but the main thing is good teams come out of slumps quicker than others and we have to come out the quickest we can," White Sox manager Ozzie Guillen said.
Trailing 1-0, the Rangers tied the game in the third inning on a sacrifice fly by Wilkerson. With two outs and a runner on, Buehrle walked Ian Kinsler and Young followed with his eighth homer, a three-run shot to left. Three pitches later, Teixeira followed with his 13th home run to left-center, giving the Rangers a 5-1 lead.
The Rangers have hit consecutive home runs eight times this season.
"Buehrle is tough. He's always been tough on me," Young said. "I haven't really been following his last couple of starts, but that's the least of my concerns. As far as I'm concerned he's still one of the best in the league and always will be. We know every time we face him we have our work cut out for us."
Buehrle (9-8) was booed as he walked back to the dugout after retiring the Rangers in the third. He pitched seven innings, allowing five runs and seven hits. He had four strikeouts and walked two.
"It just seems when you are going good everything is going your way, when you're going bad everything drops in and when you make your pitches they hit them," Buehrle said. "I think the last three innings I threw more pitches down the middle and got away with them than I did earlier in the game, so it's a weird game."
Young added an RBI double in the eighth off White Sox reliever David Riske and Mench made it 9-3 with the three-run homer off Neal Cotts. Mench was 3-for-4 with three RBI, while Young finished with four RBI.
"Mikey had a big night. He squared up a lot of balls," Rangers manager Buck Showalter said of the All-Star game MVP.
Ron Mahay (1-1) earned the victory for the Rangers with two scoreless innings.
Rick Bauer pitched 2 1/3 hitless innings for his second save.
With two outs and nobody on in the sixth, Mahay was replaced by Wes Littleton, who gave up Crede's 20th homer that cut the Rangers' lead to 5-3.
Thome hit his 32nd homer of the season on a 2-0 pitch in the first inning off John Wasdin. Thome tied Jose Canseco for 27th on the all-time list and gave the White Sox a 1-0 lead.
- Rangers 3B Hank Blalock got the night off from the field and was the DH. He was 0-for-4.
- Wasdin pitched 3 2/3 innings, allowing two runs and five hits. He struck out four and walked two.
- Mahay won his first game since Sept. 11, 2004.