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BOSTON (AP) — That's the Ryan Dempster the Texas Rangers hoped they got at the trade deadline.

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.

"Anytime you have a rough one you want to get out there the next day," Dempster said. "Those five days take a long time. I think just knowing the lineup a little bit facing these guys. I was able to use the fastball and had a good split."

Dempster (1-0) allowed three unearned runs, six hits, struck out six and walked one in 6 2-3 innings.

Acquired from the Chicago Cubs minutes before last week's non-waiver trade deadline, he was tagged for eight runs in 4 2-3 innings by the Angels in his first Rangers' start on Thursday.

On Tuesday, he showed why he was the one of the top prizes at the deadline.

"Even though he gave up all those runs against Anaheim, he kept us in that ballgame and we won that ballgame," Rangers manager Ron Washington said. "He had a two-point-something ERA, leading the National League in ERA, leading the National League in (batting average) against. We know he's capable of getting outs, and he proved that tonight, without a shadow of a doubt. We're very happy to have him. We certainly need his leadership in the front part of our rotation."

Rangers outfielder David Murphy knew how Dempster felt, having been dealt by Boston to the Rangers at the deadline in 2007.

"He's a veteran and he's an easygoing guy to begin with, but I think as a man you want to earn your keep," he said. "Obviously after not having his best stuff his first outing, he wanted to turn that around as quickly as possible. I think he did that tonight."

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.

Jon Lester (5-10) gave up four runs on six hits in 6 2-3 innings. He's 0-5 in his last six starts.

"It's another heck of a performance. We didn't score the runs and he didn't get the breaks," Red Sox manager Bobby Valentine said. "Couple of curveballs to a couple of left-handers wound up hurting him."

Lester, expected to be one of the club's top starters, hasn't won since June 27.

"I can't keep talking about being frustrated and all this stuff," he said. "Everybody obviously knows here that we're frustrated and we don't like losing. ... But there's positives for me personally in this game that I'm going to take and go forward to the next one."

Boston's Dustin Pedroia was called out on an attempted check swing by first base umpire Paul Nauert in the eighth and ejected in the top of the ninth.

"It looked like he checked his swing from our vantage point," said Valentine, who came out after his second baseman was tossed.

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.

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, 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.

NOTES: Rangers SS Andrus was back in the lineup after missing Monday's game with a sore right shoulder. ... Texas C Mike Napoli didn't start after catching four straight games. ... Boston's David Ortiz, on the 15-day DL since July 18 with a strained right Achilles, took batting practice on the field and said hopes to return this weekend when the Red Sox play in Cleveland. ... For the second straight day, Rangers OF Hamilton spent a long time signing autographs, posing for pictures and joking with the fans on the field next to Texas' dugout during BP. ... Boston RHP Clay Buchholz wore a large Frisbee-type disc around his neck for a good portion of BP. ... Shawn Thornton, Tuukka Rask and Daniel Paille of the Boston Bruins took BP on the field about 3½ hours before the game.

ABILENE, Texas (AP) — Police in West Texas have shot and killed a gunman who allegedly slipped into his estranged wife's home by removing an air conditioner.

Abilene Police Chief Stan Standridge says the man died at a hospital following Wednesday morning's shooting. The wife wasn't hurt.

The woman called 911 to say her estranged spouse was in her bedroom. Police say the man apparently removed a window air conditioning unit to get inside and threatened to kill her. He then allegedly walked to the backyard.

Standridge says the 49-year-old man, whose name wasn't immediately released, had a loaded revolver. The suspect allegedly pointed the gun at officers and wouldn't surrender.

Both officers opened fire and shot him several times.

The officers have been put on administrative leave during a review of the incident.

DALLAS (AP) — Dallas police say a 16-year-old girl who was in her room has been shot after someone outside her home opened fire on the residence.

Police say five other people suffered minor injuries from flying glass during the incident early Wednesday.

Investigators say no one has been arrested. Police are trying to determine a motive for the attack. Several bullets went into the residence.

Police say the girl was asleep but awoke when she heard several gunshots from outside. The teen was shot in the torso but police say she was in good condition when transported to a Dallas hospital. Her name hasn't been released.

Further details were not immediately available.

Republican National Committee Chairman Reince Priebus said Wednesday that the former state solicitor general will address the Aug. 27-30 convention along with four other conservative notables, including Wisconsin Gov. Scott Walker.

Cruz is a tea party darling who upset Lt. Gov. David Dewhurst for the Republican nomination to replace retiring U.S. Sen. Kay Bailey Hutchison.

Dewhurst was backed by Gov. Rick Perry and much of the Texas GOP establishment but lost a July 31 runoff election to Cruz by 13 percentage points.

Cruz advances to the November election against Democratic former state Rep. Paul Sadler. Texas hasn't elected a Democrat to the U.S. Senate since Lloyd Bentsen in 1988.

Internal affairs officers are reviewing Tuesday afternoon's shooting. Police say the officer who fatally shot the suspect has been with the force since 1984.

Police say a 911 call from the woman, who had a restraining order against her husband, summoned officers.

Investigators say the suspect, who briefly ducked into a waiting taxi he apparently took to the building, refused to put down a pistol and threatened to harm his spouse. An officer shot the husband before the suspect could enter the woman's building.

Houston police believe the gunman, whose name was not immediately released, was also responsible for a shot fired into the building early Tuesday.