Norris, who made his first Grapefruit League appearance, allowed just one baserunner, with a walk to Jim Thome in the second inning. The Astros had been lucky against Phillies right-hander Vance Worley, who scattered five hits and allowed two runs in two innings in his Spring Training debut.
Astros center fielder Jordan Schafer singled and scored in the first inning to make it 1-0. Jed Lowrie walked and later scored on a Jason Castro single in the second inning to make it 2-0.
Houston punished the Phillies' pitching all afternoon, with Schafer finishing 3-for-4 with two runs and an RBI and J.D. Martinez contributing a 2-for-4 effort with three RBIs.
Pat Misch and Dontrelle Willis took the brunt of the Astros' output in relief of Worley. Misch allowed four runs (one earned) on five hits, and Willis allowed four runs on three hits.
Jonathan Papelbon got in an inning, pitching a scoreless fifth.
The Phillies didn't strike until the eighth, with Lou Montanez driving in a pair of runs on a double. Hector Luna added a run in the ninth on a homer for the final margin.
Up next: The Phillies host the Pittsburgh Pirates at 1:05 p.m. Thursday at Bright House Field in a game available live on MLB.TV. Phillies left-hander Cole Hamels will be making his second Grapefruit League start. Dave Bush, Antonio Bastardo, David Purcey and Phillippe Aumont are also scheduled to pitch.
Todd Zolecki is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.