The Cardinals trailed 16-0 after three quarters and scored all their points in the fourth quarter.
Beanie Wells scored on a 2-yard TD pass from Derek Anderson and Alfonso Smith rushed 6 yards for a score for Arizona.
Matt Leinart was 6-of-7 passing for 49 yards. Anderson finished 13-of-22 passing for 88 yards.
Texans quarterback Dan Orlovsky was 12-of-21 passing for 129 yards. Houston starter Matt Schaub was 5-of-6 for 78 yards and a 44-yard TD pass to Andre Johnson.