Cruz's two-run blast in the sixth ignited a six-run outburst that put the Rangers ahead 7-3, but it was Berkman's solo shot in the next frame off Phil Humber (0-8) proved to be decisive run.
Leonys Martin added a two-run triple during the sixth-inning uprising for Texas, which clinched its three-game series.
Yu Darvish (6-1) yielded four runs on four hits over eight full innings to record the win, walking three and striking out nine.
Trevor Crowe greeted him with an RBI single and the Astros scored another run when Nathan uncorked a wild pitch, with Crowe going to third.
Marwin Gonzalez delivered a sacrifice fly, but after Robbie Grossman walked, Nathan retired Chris Carter for the final out and his 11th save.
Matt Dominguez slammed a pair of homers for the Astros.
Swim Week Miami Beach 2014 [PHOTOS]