The loss snapped an eight-game losing streak for Chicago, which had not put up more than two runs in a game since June 13.
"Any time you go on a skid like this, it's always nice to get [the win]," said White Sox manager Robin Ventura. "You get that feeling away from you. But you can only feel good about it for a little while, and you get back after it. You have to be able to continue momentum with it, but there's a game tomorrow. So these guys will be preparing for tomorrow."
Rodon picked up his fifth quality start in six outings, allowing two earned runs and four hits with five strikeouts across six innings. The left-hander Rodon rebounded from a rough start at Pittsburgh when he allowed seven earned runs in 3 2/3 innings of work. He gave up both runs in the fifth inning on a single and fielder's choice, otherwise limiting baserunners for much of the contest.
"Today more than anything, Rodon had his fastball and got us to swing at some breaking balls down," Rangers manager Jeff Banister said. "He took advantage of a low strike zone."
The White Sox added three runs in the third inning to provide the run support, but the Rangers' Nick Martinez managed to find his way out of a jam to limit the damage. Martinez surrendered two earned runs and six hits in six innings, but he left the bases loaded three separate times.
After he blew a save on Friday night, White Sox closer David Robertson closed the door on Prince Fielder and Mitch Moreland in the ninth for his 14th save of the season. He capped off a strong performance with relievers Zach Putnam and Zach Duke, who also didn't allow a baserunner.
"I was definitely giving it everything I had," Robertson said. "I was not going to give in at any point. Those are good hitters. You have to be careful. I had good stuff today. I didn't miss many pitches, which is nice."
MOMENTS THAT MATTERED You get a single: The White Sox hadn't put up three runs in a game since June 13, but they tacked on three in the third inning thanks to three singles to begin the inning. Adam Eaton, Avisail Garcia and Jose Abreu each singled and scored in the inning. Adam LaRoche hit a sac fly to score one while Garcia and Abreu came home on an error by Rangers shortstop Elvis Andrus.
Andrus errors costly: Andrus made two errors in the game. It's the eighth time in his career he has committed two errors in the game. The first one was huge. The White Sox, with one run in, had the bases loaded with one out in the third when Alexei Ramirez hit a bouncing grounder up the middle. It should have been an inning-ending double play, but the ball hit off Andrus' glove and into center field. Two runs scored on the play.
"I should have made that play," Andrus said. More >
Offensive power outage: For the third straight game, the Rangers weren't able to deliver at least one extra-base hit. They have also scored in just three of their past 32 innings. Their last extra-base hit was a home run by Prince Fielder in the ninth inning on Wednesday.
Leaving them loaded: The White Sox loaded the bases in three different innings, but stranded all three runners each time. Two of those times, Carlos Sanchez picked up the final out to end the inning. Chicago went 1-for-8 with runners in scoring position, and is now hitting .165 (14-85) with RISP over the past 15 games.
"That'll happen," LaRoche said. "You get them out there enough times, you're going to score runs. … Obviously, the more opportunities you have, your odds go way up. The past two weeks, it seems like we'll have one or two big opportunities a game and that's it. It's tough to win like that."
QUOTABLE "He continues to want to go back out there, and I think that's the stuff we're learning about him, his maturity and composure and competitiveness, it's great to see" -- Ventura, on Rodon's start to rebound from his last outing
SOUND SMART WITH YOUR FRIENDS Martinez hit three batters, tying the club record. He is the 12th pitcher to do so, although Charlie Hough did it twice. Martinez has 12 hit batters for the season, the most in the American League. The record is 19 set by Hough in 1987. Martinez is currently tied for 10th most.
REPLAY REVIEWS In the bottom of the first inning, Chicago's Melky Cabrera jumped in pain on a pitch that went inside from Martinez. Originally ruled a ball, Cabrera insisted he was hit and prompted manager Robin Ventura to challenge the call. After a lengthy review, umpires overturned the ruling and awarded Cabrera first base.
The big one came in the seventh inning when Martin, batting with one out and nobody on base, hit a long high fly into the right-field bleachers that was called foul by first-base umpire Gerry Davis. The Rangers asked and were granted a crew chief review, hoping the call would be turned into a game-tying home run. Instead, the call was upheld. More >
WHAT'S NEXT Rangers: Right-hander Yovani Gallardo pitches against the White Sox at 1:10 p.m. CT Sunday. Gallardo is 3-0 with a 1.41 ERA in his last five starts with opponents hitting .179 off him.
White Sox:Jose Quintana takes the mound Sunday, looking for his fifth straight quality start when the White Sox host the Rangers at U.S. Cellular Field at 1:10 p.m. CT. Quintana has picked up one win that span, allowing an average of two runs a game.