Norris allowed three hits and one run in a 12-0 loss to the Cubs on the day he was scheduled to start for Triple-A Round Rock. The No. 2-ranked prospect in the Astros' farm system could start in place of Oswalt, who left Tuesday's game in the second inning with a left lower back strain and flew to Houston to be examined.
"He will give us protection for Sunday in the event Roy can't make his start," Astros general manager Ed Wade said. "Obviously, we've been paying a lot of attention to what he's being doing at Triple-A and are very pleased with the results there.
"On one hand, we're anxious to get him to the big leagues to see how he can perform at this level, but at the same time the guys who have been here are performing pretty well, so there wasn't a real great sense of urgency to do something."
To make room for Norris on the roster, the Astros optioned infielder Edwin Maysonet back to Triple-A Round Rock. He was called up Friday and appeared in only one game because he was gone from the team for a few days to be with his wife in Puerto Rico when she gave birth.
Norris, 24, was 4-9 with a 2.63 ERA in 19 starts at Round Rock this year, allowing 104 hits, 53 walks and striking out 112 batters in 120 innings.
Norris, who didn't make the Astros out of Spring Training, went to Round Rock and worked with pitching coach Burt Hooton on establishing a third pitch to go along with his hard fastball and slider -- a changeup.
"I think that was the big key, and obviously being healthy," Norris said. "This was the first year I've been really healthy and have had an opportunity to get out there and put up consecutive starts, and that's been great. It gives me that extra confidence in the back of my head knowing I can go out there and give my team an extra effort every time and consistently every five days."
Norris said Hooton told him not to change anything when he reached the Majors.
"He said, 'You've got a great fastball and attack the zone and pound the lower half. You don't really need to change much. Just work with your catchers and do the best you can,'" Norris said.
Brian McTaggart is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.