Littleton worked out of a bases-loaded, nobody-out jam in the eighth, and Marlon Byrd hit a tiebreaking single in bottom of the inning to send the Rangers to a 4-3 victory over the White Sox for Texas' third straight win on Tuesday night.
"He stood up like a man," Washington said. "He got us two ground balls to get out of the inning. He kept his composure. He made pitches when he had to with his sinker. He did exactly what you're supposed to do. He didn't panic."
Ian Kinsler and Gerald Laird homered for the Rangers, who have won five of their last seven.
Chicago's Jim Thome homered to move within six of becoming the 23rd player in the 500 club and went 2-for-2 with a pair of walks. Paul Konerko also connected for the White Sox, who have lost seven in a row on the road.
Littleton (1-1) pitched one inning of relief for the decision, getting Juan Uribe to ground into a forceout at the plate, and rookie Danny Richar to ground into an inning-ending double play.
"It's the same situation whether you're up one run or 27, I'm thinking no runs," said Littleton, thinking back to last week's blowout of the Orioles. "No matter how many runs you're up you have to make pitches. I just wanted to slow the game down. I needed ground balls."
Littleton got a three-inning save in the Texas Rangers' modern major league record 30-3 rout at Baltimore last week.
With the score tied at 3, Michael Young led off the Texas eighth with a single and moved to second on Mike MacDougal's wild pitch. Byrd followed with a single up the middle off MacDougal (1-4) to score Young from second.
"I fell behind 0-2 quickly," Byrd said. "I just tried to battle. I got a good pitch that I put in the right spot."
White Sox manager Ozzie Guillen has seen his team fail to come through with the big hit all season, and he saw more of the same in the top of the eighth.
"That's why we lose games," Guillen said after the White Sox were beaten for the 14th time in their last 17 games. "We have the bases loaded, nobody out, and we have the worst at bats. You need the best at bats you can get. When you don't score in that situation, the other team is going to take advantage."
Joaquin Benoit pitched the ninth for his second save in six chances.
Konerko was in a 2-for-22 slump before sending Kason Gabbard's 2-2 pitch into the Rangers' bullpen for his 27th homer of the season and a 2-0 lead in the first.
Thome's 22nd homer, a 422-foot solo blast off the back wall in the Texas bullpen in the third, was the 494th of his career to extend Chicago's lead to 3-0. That moved Thome out of a tie on the all-time list with Lou Gehrig and Fred McGriff and into sole possession of 23rd place. Next up for Thome is Eddie Murray with 504.
Kinsler's third-inning bases-empty shot, his 17th of the season, pulled Texas within 3-1. Laird's eighth homer, a two-run blast in the fourth, tied it at 3.
Gavin Floyd gave up gave three runs and six hits over six innings for the White Sox.
"Floyd attacked the strike zone and kept us in the game," Guillen said.
Gabbard allowed three runs and four hits in 4 2/3 innings. He was making his sixth start for the Rangers since he was acquired in a trade with Boston on July 31 that sent Eric Gagne to the Red Sox.
Texas 3B Travis Metcalf strained his left hamstring while running out a bunt attempt in the seventh. He was replaced by Ramon Vazquez. ... Floyd was making his fifth start of the season for Chicago. ...Thome's two walks give him 1,444 for his career, tying Eddie Matthews for 20th on the all-time list. ...Benoit had his first save since April 28 against Toronto, and third of his career. ...The Rangers held the White Sox scoreless on three hits after the third inning.