Palmer compiled 241 aerial yards with an interception on 20-of-32 efficiency as the Cardinals (5-4) won for the fourth time in six games.
Andre Roberts (five receptions, 72 yards) and Robbie Housler (four receptions, 49 yards) each made a scoring grab for Arizona.
The Texans (2-7), meanwhile, extended their slide despite a trio of touchdown passes from Case Keenum, who went 22-of-43 for 201 passing yards.
Andre Johnson hauled in two of Keenum's TD tosses.
Notable deaths of 2014 [PHOTOS]