Erick Aybar led off the seventh with a bunt single off Texas starter Yu Darvish (7-3) and one out later stole second. Mike Trout then hit a grounder that Aybar barely avoided before it was fielded by shortstop Elvis Andrus, who argued unsuccessfully it hit the runner.
Trout stole second and Aybar scored when Callaspo delivered a solid hit to right, chasing Darvish.
With Koji Uehara pitching, Kendrys Morales hit a fly to right field that was caught by Nelson Cruz. Trout came home after the catch and barely beat the tag by catcher Yorvit Torrealba, who argued vehemently against the call.
Home plate umpire Tim McClelland ejected the Texas catcher.
Bobby Cassevah (1-0) earned the win and Ernesto Frieri picked up his fourth save for the Angels, who clinched their three-game series against first-place Texas and moved within 3 1/2 games of the Rangers in the American League West.