The winner was reliever Randy Choate (1-0).
Lance Cormier earned his second save.
Nelson Cruz led Texas with two hits -- one a two-run homer. Marlon Byrd hit a solo homer, while Ian Kinsler and Elvis Andrus had one RBI apiece for the Rangers, who scratched out seven hits and fell six games back of the AL West-leading Los Angeles Angels.
The Rangers' loss, combined with the Angels' win over Oakland Sunday, reduced LA's magic number for clinching the division to two -- as the Rangers travel to Anaheim for a four-game series with the Angeles beginning Monday.
The Rangers trail Boston by six games in the AL wild-card chase.
The losing pitcher was Frank Francisco (2-3).