Norris (5-4) logged his third straight quality start, scattering four hits and three walks over six innings. The right-hander struck out six.
Jose Cisneros followed with two shutout relief frames and Jose Veras picked up his 10th save for Houston, which notched a second straight victory over Los Angeles.
Chris Carter supplied the Astros' offense with a two-run homer in the seventh.
The loss was hung on the Angels' Jerome Williams (4-2), who yielded a pair of runs on three hits and three walks in seven innings. He fanned six.