BOSTON -- By the end of Tuesday night, the Boston Red Sox had fallen into third place in the American League East.

Yet they were the ones with six representatives -- and possibly a seventh -- in next week's All-Star game, while the team with the majors' best record is only sending two.

But the Texas Rangers didn't feel the least bit slighted.

"No one's keeping score of that," said Rangers center fielder Ian Desmond, one of Texas' two AL All-Stars along with southpaw Cole Hamels.

The scoreboard at Fenway Park certainly didn't Tuesday night, with the Rangers earning the 7-2 win over the Red Sox.

"When the season's over, no one's going to look back and say 'that team had seven All-Stars' or 'that team had two All-Stars,'" Desmond said.

"It's going to be this team won the World Series and everyone else came in second."

Boston (45-38) leads the AL with four starters in next Tuesday's annual midsummer classic in San Diego, with retiring designated hitter David Ortiz, shortstop Xander Bogaerts, right fielder Mookie Betts and center fielder Jackie Bradley Jr. starting at their respective positions.

Knuckleballer Steven Wright and closer Craig Kimbrel were named AL reserves, while second baseman Dustin Pedroia is one of five 'Final Vote' candidates who could also be making the trip.

Meanwhile, Desmond and Hamels are the lone pair of Rangers recognized from the Lone Star State, despite toting the league's best record (53-32), which they reclaimed after the Chicago Cubs' 9-5 loss to Cincinnati.

Texas' seven-run output was highlighted by Robinson Chirinos' three-run home run in the ninth, which came after Rougned Odor doubled home the go-ahead run three frames earlier.

It was the sixth homer of the year for Chirinos, the Rangers' No. 9 hitter.

"Obviously the way we won tonight, contributions up and down the lineup," Rangers manager Jeff Banister said. "Five innings out of our bullpen, solid effort by (starter) A.J. (Griffin) -- a lot of deep counts tonight, but I think the way we won -- very challenging early, held on."

Shin-Soo Choo hit a solo homer for his seventh bomb of the season and Elvis Andrus and Jurickson Profar each had RBIs for the Rangers.

Griffin labored through four innings, throwing 96 pitches while allowing two runs, seven hits and three walks with three strikeouts. Cesar Ramos (3-3) claimed the win.

Only two of Boston's All-Stars made an impact Tuesday, as first-time selection Bradley belted a solo home run, his 14th homer of the year, and fellow first-timer Bogaerts had an RBI.

Boston (45-38) earned its ninth loss in 15 games.

"We had ample opportunity, with runners on base in almost every single inning," Red Sox manager John Farrell said. "A missed opportunity tonight.

Red Sox starter David Price (8-6) lasted eight innings and struck out 10 but was a hard-luck loser as his three runs, eight hits and a walk proved beatable.

It was Price's eighth game with eight or more strikeouts this season, tied for the major league lead.

"I'm tired of this," Price said after taking his fifth loss in his last seven starts. "It's not me. I've got to get better."

Kimbrel unraveled in the ninth as he gave up an RBI single to Profar and the towering home run that bounced off the light tower in left to Chirinios.

"In 12 pitches, a lot happened," Farrell said of Kimbrel, whose ERA ballooned to 3.66 -- it was 2.53 entering the night.

Choo blasted a first-pitch homer off Price for his fourth leadoff shot of the season -- they've all come in his last 12 games -- and the 20th of his career.

Andrus' sacrifice fly brought home another run in the frame.

Boston has been outscored 30-2 in the first inning since June 12.

Bradley's leadoff blast to center in the second brought the Red Sox within a run.

Bogaerts worked a bases-loaded walk with two outs in the fourth to knot the score.

Odor's RBI two-bagger in the sixth broke the tie.

Price got Ian Desmond to strike out swinging leading off the fifth, marking his 1,500th career strikeout.

Choo left the game in the bottom of the inning with lower-back stiffness and will be reevaluated Wednesday morning.

NOTES: Texas 1B Mitch Moreland (right calf tightness) did not start for the third straight game. ... Boston activated C Ryan Hanigan from the 15-day disabled list and optioned C Christian Vazquez to Triple-A Pawtucket. Hanigan missed 26 games with a neck strain. ... Rangers RHP Yu Darvish (shoulder and neck) will throw a bullpen session Thursday and might make his next rehab start this weekend. ... Texas traded OF Ryan Strausborger to Seattle for a 2016 international draft slot compensation. The team also recalled RHP Jose Leclerc from Triple-A Round Rock and designated LHP Michael Roth for assignment. ... Red Sox RHP Brandon Workman (Tommy John surgery) began a rehab assignment with the GCL Red Sox. Workman hasn't pitched since Sept. 18, 2014. ... Boston hired former major-leaguer Brian Banister as an assistant to pitching coach Carl Willis. ... Rangers LHP Martin Perez (7-4, 3.39 ERA) opposes Red Sox RHP Steven Wright (9-5, 2.42 ERA) in Wednesday's finale.