Ogando (4-2) logged his fifth straight quality start, holding the Athletics to two runs on four hits. The right-hander walked one and struck out three.
Cruz's blast in the fifth inning handed the Rangers a 6-0 advantage.
Lance Berkman contributed a two-run single in the first as Texas cruised to a victory in the rubber match of a three-game series.
A's starter Daniel Straily (1-2) was tagged for five runs (four earned) on four hits over 4 1/3 innings. He walked four and struck out two.
Coco Crisp and Derek Norris each drove in a run for Oakland.