The right-handed Norris, who upped his record to 6-13 with the win, pitched 7⅓ scoreless innings and allowed only two hits while striking out seven. Norris got into some trouble in the eighth after a hit-by-pitch and an error put two Cardinals (84-72) on with no outs. Wilton Lopez came in to relieve Norris and drew two groundouts to get out of the jam.
Houston (51-105) scored both of its runs in the fourth inning off Cardinals starter Chris Carpenter (0-1). Jose Altuve led off the inning with his sixth home run of the year, and Houston eventually pushed across first baseman Brett Wallace four batters later.
The Astros will enjoy an off day Thursday before closing out the season on the road against the Milwaukee Brewers and Chicago Cubs.