The White Sox (40-25), who are averaging 5.32 runs per game and outscored the Rangers 13-5 to win the first two games of this series, lost 8-0 on Wednesday.
Chicago was held scoreless for only the second time this season, and managed a season-low four hits—all singles.
The last time the White Sox were shut out—against Cleveland on May 31— they came back to score eight runs against the Indians the following day.
Rangers rookie left-hander John Rheinecker (2-0, 2.42 ERA) makes his fifth major league start on Thursday.
Rheinecker held the White Sox offense in check less than two weeks ago, allowing just two runs and seven hits in eight innings of a 10-2 victory on June 4, his second career win.
“It’s a confidence booster,” Rheinecker said after that contest. “Hopefully, the team is getting confident in me. I’m just as confident in them that they’re going to score runs.”
The rookie allowed three runs and nine hits in 5 2-3 innings in the Rangers’ 7-4 win at Boston on Saturday, but did not factor in the decision.
White Sox left-hander Mark Buehrle (6-4, 3.21) started against Rheinecker on June 4, and will oppose him again on Thursday as he looks to avoid losing to the Rangers for a third straight time.
After going 7-0 with a 1.79 ERA in his first seven career starts against Texas, Buehrle is 0-2 with a 6.43 ERA in his last two outings.
He allowed six runs and nine hits in seven innings in the loss on June 4, his only game against the Rangers (35-31) this season.
Buehrle has lost his last two decisions overall. He pitched well on Saturday against Cleveland, giving up two runs and six hits in eight innings, but did not record a decision in a contest Chicago won 4-3 in 11 innings.
“I needed that game, just for myself, for my head,” said Buehrle, who had allowed 10 runs over 13 innings to lose his prior two starts. “Even though you know you’re going to have your bad outings and your tough stretches, it’s frustrating when you do have them.”
The Rangers lead the AL West by a half-game over Oakland after winning just three of their last eight.
Leadoff hitter Gary Matthews Jr. had three hits on Monday for his third consecutive multihit effort, and is hitting .459 (28-of-61) over the past 13 games.
Michael Young extended his season-high hitting streak to 13 straight games with two singles on Wednesday, and is batting .323 (20-for-62) during the run.
Young has struggled against Buehrle, though, batting just .188 (6-for-32) against the left-hander.