Norris pitched three-hit ball over seven innings, Rick Ankiel drove in three runs and Justin Maxwell hit his first home run of the season, leading the Astros to a 5-0 victory over the Los Angeles Angels on Friday in their first meeting as AL West rivals.
"I've had those kind of starts before in my career and I know I've got more left in me," Norris said. "It's not like anything changes. You try to do it every time and it's not necessarily going to go down that way."
Norris (2-1) struck out five and walked two in his 100th big league start, helping the Astros win their third in a row after six straight losses.
Rookie manager Bo Porter used three relievers in the ninth to clinch the combined four-hitter.
"This guy's a No. 1 starter and he's pitched a lot of big games," Porter said. "I think his best years are definitely ahead of him. He's growing up right in front of our eyes, and it's a pleasure to see."
The Angels, coming off a three-game sweep by Oakland, have lost five straight and are off to a 2-8 start -- matching the worst in franchise history.
The inaugural 1961 club also lost eight of its first 10.
"That's obviously a bad play. That's a mental mistake," manager Mike Scioscia said. "As perfect as players try to play, and as hard as they try to play, unfortunately mental mistakes are occasionally going to creep into the scenario.
"We've seen it from other teams, and unfortunately it got us tonight. And Josh knows it. He's accountable. He knows he messed up. So we're going to move on. It's a mental mistake. It happens. It's obviously ugly when it happens, and we're going to move on. That's it."
Tommy Hanson (1-1) threw 108 pitches through five innings, giving up five runs, eight hits and two walks.
The Angels, who have a $148.5 million payroll, have had their rotation struggle on this homestand.
Ace right-hander Jered Weaver is on the disabled list for at least a month because of a broken bone in his left arm.
Garrett Richards will come out of the bullpen to make his first start of the season on Saturday.
Hanson gave up hits to his first four batters and threw 27 pitches before retiring anyone.
Jose Altuve singled and scored on a drive to right-center by Justin Maxwell, who was thrown out trying for a triple. TV replays showed that umpire Laz Diaz got the call wrong, as Luis Jimenez took the relay throw from second baseman Howie Kendrick and applied the tag after Maxwell's foot hit the bag.
Castro and Chris Carter followed with singles, and both runners advanced when Hanson attempted to pick off Castro and shortstop Brendan Harris mishandled the throw for an error. A full-count walk to Carlos Pena loaded the bases for J.D. Martinez, who struck out. But Ankiel grounded a two-run single just past shortstop on Hanson's 35th pitch, giving Houston a 3-0 lead.
Maxwell, who led the Astros last season with 18 homers, made it 4-0 in the second inning with a drive to left-center on a 2-1 pitch. It was the 18th home run given up in 90 1/3 innings this season by a Angels pitching staff that has a 5.38 ERA.
Ankiel, playing for his fifth big league club after signing a minor league contract with the Astros and getting an invite to spring training, completed the scoring with an RBI double in the third.
The Angels paid tribute to their late public address announcer, David Courtney, with a pregame moment of silence. Courtney died Nov. 29. His widow, Janet, threw a ceremonial first pitch -- wearing a No. 19 Angels jersey that signified the years her husband spent behind the microphone at the "Big A." ... The Astros had a 3-3 interleague record against the Angels and were 1-2 in their only series at Anaheim in June 2007. ... Jimenez, the Angels' top rookie in spring training, made his major league debut after getting called up from Triple-A Salt Lake because of injuries to 3B Alberto Callaspo and SS Erick Aybar. OF J.B. Shuck was optioned to Salt Lake. ... Astros 1B Brett Wallace, 0 for 9 with five strikeouts against Hanson, sat out for the second straight game. He is 1 for 21 this season with 17 strikeouts.