BOSTON (AP) -- Ryan Dempster rebounded from a rough debut with Texas by pitching shutout ball into the seventh inning, Ian Kinsler had a pair of RBI singles and the Rangers snapped a two-game losing streak with a 6-3 win over the Boston Red Sox on Tuesday night.
Josh Hamilton and Nelson Cruz each had two hits and drove in a run for Texas.
Will Middlebrooks had a pinch-hit three-run homer for the Red Sox, who have lost five of seven.
The AL West-leading Rangers have lost three straight only three times this season.
Dempster (1-0) gave up Middlebrooks' homer after a two-out error by Kinsler. He allowed three unearned runs, six hits, struck out six and walked one in 62 3 innings.
Jon Lester (5-10) gave up four runs on six hits in 62 3 innings. He's 0-5 in his last six starts.
Boston's Dustin Pedroia was called on an attempted check swing by first base umpire Paul Nauert in the eighth and ejected in the top of the ninth.
Dempster, acquired from the Cubs minutes before last week's non-waiver trade deadline, was tagged for eight runs in 42 3 innings by the Angels in his initial Rangers' start last Thursday.
On Tuesday, he showed why he was the one of the top prizes at the deadline.
Until Middlebrooks belted his homer, it was very similar to when Dempster faced the Red Sox earlier this season.
He mixed a sharp splitter with a well-spotted fastball to keep Boston's hitters off-balance most of the night.
Joe Nathan worked the ninth for his 22nd save.
With Texas leading 4-0 and two outs in the seventh, Kinsler misplayed Ryan Kalish's grounder for an error. Middlebrooks followed by hitting the first pitch over the Green Monster -- where a fan reached out to grab the ball near the top of the wall. The call was reviewed and upheld after a lengthy review.
Cruz's RBI single made it 5-3 in the eighth. Hamilton's single made it 6-3 in the ninth.
Dempster worked seven shutout innings against Boston in Chicago's win on June 15.
The Rangers broke a scoreless tie with a pair of runs in the sixth. After taking a close pitch for a ball with a 1-2 count, David Murphy had a leadoff double. One out later, Kinsler singled off the top of the left-field wall, advanced on a groundout and scored on Hamilton's single to right.
In the seventh, Murphy had a sacrifice fly and Kinsler added an RBI single, making it 4-0.
Carl Crawford doubled in the first, but was picked off second. Cody Ross opened the second with a double, but was stranded.
Dempster then retired 14 of the next 15 -- allowing only Ross' two-out double in the fourth -- until he walked Pedroia in the sixth.
The Red Sox were coming off an eight-double game in Monday's win and three of the first four balls they hit into play Tuesday night were off the Monster, including two doubles.