Texas rookie starter Tommy Hunter (2-1) gave up only one run over six innings for the win, while Boston starter and Texas native Josh Beckett (11-4) was denied his 101st career win.
"That was great," Rangers outfielder Marlon Byrd told reporters. "Beckett was Beckett—just like he always is. To beat him, you have to have your pitcher go out there and match him, and that's what Tommy did."
Boston's loss, coupled with the Yankees' 6-4 triumph over Baltimore, dropped Boston a game behind New York in the AL East. They had been tied for first before Tuesday's games.
The loss was the Red Sox's fourth in a row while the Yankees have won five consecutive.
Hank Blalock put the Rangers on the road to their third consecutive victory with a two-run single in the first inning.
Kevin Youkilis brought the Red Sox within a run with a sixth-inning double, but Texas came back with solo runs in the seventh and eighth innings.
Mike Lowell added Boston's second run with a single in the ninth.
Hunter struck out two and walked one while allowing four hits. Three relievers limited to one run and one hit.
Hunter had been shelled in an August 2008 game in Boston, giving up nine runs on seven hits in less than 2 innings.
The difference, he said, was his ability to throw a variety of pitches.
"I have four pitches (now)," Hunter said. "Last year, I had just 1 and a half pitches. I didn't even have my fastball, because it was up in the zone.
I threw a lot of changeups (tonight). They didn't see that last year. When you throw four pitches for strikes, you do pretty well."
Beckett was tagged for four runs and seven hits in a complete game performance. He struck out seven and walked only one.
"I didn't make very good pitches," Beckett said. "This one definitely falls on me."
But team mates did not see it that way, especially after Beckett settled down after the two-run hit to Blalock, retiring 14 batters in a row before Andruw Jones doubled in the seventh inning.
"We have to do a better job," said Red Sox second baseman Dustin Pedroia. "This is an offensive ballpark. We have to score more runs."
