Robbie Ross, Tanner Scheppers and Michael Kirkman allowed one hit combined in the next 1 2-3 innings. Closer Joe Nathan struck out the side in the ninth.
Houston starter Philip Humber (0-1) yielded five hits and a run in 5 2-3 innings in his Astros debut.
Nelson Cruz and A.J. Pierzynski had two hits apiece and drove in a run each for the Rangers.
Ogando returned to the rotation this season after spending last year in the bullpen, where he had a career-high 58 relief appearances.
He retired nine straight Astros before Carlos Pena singled with two outs in the sixth inning. Chris Carter lined out to end that inning, and Houston’s next hit, a one-out single in the seventh by Justin Maxwell, chased Ogando.