Norris entered the game with a 10.29 ERA in three appearances, but said he felt relaxed and ready for opening day after shutting down Cardinals.
Astros manager Brad Mills said he did not realize that Norris had struggled this spring. He said Norris looked fine and was ready to step into one of the openings on the Astros staff. Norris went 9-10 with a 4.92 ERA for Houston last season.
The Astros were out-hit, 11-7, but took a 3-0 lead and held on. First baseman Brett Wallace improved his spring training average to .362 with a run-scoring single.
Lance Lynn started for the Cardinals and struck out four, allowing two runs in four innings.