The Rangers racked up 18 hits, Andre Beltre collecting four of them along with three RBI.
While Texas feasted on Boston's pitchers, Derek Holland tossed eight shutout innings, striking out nine Red Sox.
The win keeps Texas 1 1/2 games clear in the American League West, with Oakland keeping pace by defeating the New York Yankees 2-0 - in turn maintaining Boston's 2 1/2 game lead in the AL East despite their loss.
AJ Griffin carried a shutout into the eighth and took the win with the support of Adam Rosales' early home run.
The big-spending Toronto Blue Jays slumped to 10-20 as they lost 4-0 to the Seattle Mariners, with Felix Hernandez tossing eight scoreless innings, while Kyle Seager hit a two-run homer to punish Ricky Romero on his return to the Toronto rotation.
The Detroit Tigers reclaimed top spot in the AL Central with a 4-3 victory over Houston thanks to Alex Avila's two-run home run off Astros closer Jose Veras.
The win edges the Tigers a half game clear of the Kansas City Royals, who saw their game with the Chicago White Sox postponed due to continuing poor weather.
The Cleveland Indians edged out the Minnesota Twins 7-6 in 10 innings to edge into third place in the division.
The thus-far disappointing Los Angeles Angels showed signs of life in a 4-0 win over the Baltimore Orioles as Jason Vargas tossed a three-hit shutout.
Mike Trout had three RBI and Mark Trumbo added a home run.
In the National League, the St Louis Cardinals extended their winning streak to four games at the top of the Central Division, beating the Milwaukee Brewers 6-1 in a contest highlighted by a towering home run from Matt Holliday.
Second-placed Pittsburgh kept pace one game back with a 3-1 victory over the Washington Nationals which came courtesy of a two-run blast from rookie Jordy Mercer and another home run from Andrew McCutchen.
Cincinnati are 2 1/2 games behind the Cardinals after escaping with a 6-5 win over the Chicago Cubs despite a rare blow-up from closer Aroldis Chapman.
The Cubs lit the Cuban up for three runs but JJ Hoover came in to nail down the save, striking out Darwin Barney with the bases loaded.
The NL East-leading Atlanta Braves suffered a 7-5 extra-inning loss to the New York Mets, who twice tied the game with home runs from Marlon Byrd and David Wright before Ruben Tejada got the winning hit.
Home runs from Ryan Howard, Chase Utley and Domonic Brown powered the Philadelphia Phillies to a 6-1 victory over the Miami Marlins while the San Diego Padres held off a late Arizona rally to beat the Diamondbacks 7-6.
Buster Posey's home run at the bottom of the ninth secured a 2-1 win for the San Francisco Giants at home to the Los Angeles Dodgers.
The Giants' win meant they drew level at the top of the NL West, after the Colorado Rockies lost 7-5 to the Tampa Bay Rays.
The Rays scored three runs in the top of the 10th inning, Evan Longoria driving in the first before a two-run homer from Kelly Johnson all but finished the Rockies.