A tight back forced him out of the game before he threw a pitch in the seventh, and then the bullpen fell apart, sending the Astros to a 7-3 loss to the Kansas City Royals.
Mike Moustakas tied it with an RBI single before George Kottaras walked with the bases-loaded to drive in the go-ahead run in a four-run eighth inning, and the Royals rallied for win to end a four-game skid.
The Royals trailed 3-0 and couldn't get much going offensively until the seventh when they cut the lead to one on RBI singles by Alcides Escobar and David Lough.
Eric Hosmer chased Wesley Wright in the eighth when he singled to load the bases. He was replaced by Jose Cisnero, who gave up the one-out RBI single by Moustakas, which snapped a 0-for-18 slump. Cisnero then walked Kottaras on four pitches to put the Royals on top.
They added two more runs when Escobar grounded into a force out to score Hosmer before an error by Marwin Gonzalez allowed Moustakas to go home.
Paul Clemens (1-2) took the loss after allowing three hits and two runs while getting only one out before Wright replaced him.
"That is one of those things where you feel like you have the right matchups," manager Bo Porter said of the bullpen. "For a long time, Clemens has been great, and Wesley has been really good against lefties. Tonight, we just didn't get it done, and you have to give the Royals a lot of credit. They battled, put balls in play and had some really good at-bats late in the game."
Houston's Jimmy Paredes tied a career high with three hits, including a three-run homer in the fourth inning. Paredes, who was elevated from Triple-A on May 6, said he's starting to feel more comfortable at the plate.
"I am just trying to (have) a good approach, and to make good contact to get good base hits," he said. "I don't want to try to do too much. I am working on all my game to hopefully get better. I think tonight, I had an all right game, but I am still working."
Bruce Chen (3-0) pitched a scoreless seventh for the win.
The Royals added a run in the ninth when Elliot Johnson scored on a wild pitch by Cisnero.
Norris allowed five hits - all singles - and struck out two.
"He threw the ball well," Royals manager Ned Yost said. "It showed you how well he threw the ball; as soon as he got out of there we started our offensive outburst."
It was the second straight game Norris had left early because of back problems. He had his start pushed back two days as a precaution after he left his previous outing with lower back spasms.
"It's some tightness," Norris said. "It's unfortunate, but I have been dealing with it."
He isn't worried about the bullpen bouncing back after Tuesday's tough performance.
"This bullpen, they don't need to hang their heads at all," he said. "They know what they need to do ... I am not worried about them. They are professionals, but this one was just tough for us as a team."
The Royals didn't get a runner past second base until the seventh inning. Norris was replaced by Travis Blackley who allowed back-to-back singles by Hosmer and Lorenzo Cain. Moustakas grounded into a force out which left runners at first and third base.
Clemens took over with two outs, and Escobar greeted him with a pinch-hit, run-scoring single to cut the lead to 3-1.
A sharply hit single by Lough, which Escobar had to leap to avoid, skidded into right field and sent another run home to make it 3-2.
Kansas City starter Wade Davis yielded eight hits and three runs in five-plus innings.
J.D. Martinez hit a one-out single in the fourth inning before Carlos Pena's two-out single. Paredes then launched his first homer of the season into the seats in right field to give Houston a 3-0 lead. Matt Dominguez singled and Gonzalez drew a walk, but Davis escaped the inning when Robbie Grossman grounded out.
The Royals were foiled by their baserunning in two straight innings. Johnson singled with two outs in the third inning, but was thrown out trying to stretch the hit into a double. In the next inning, Alex Gordon led off with a single, but was later caught stealing.
Paredes walked to start Houston's sixth before a single by Dominguez chased Davis. He was replaced by J.C. Gutierrez and Kottaras, the catcher, picked off Paredes when he strayed too far from second base. Gutierrez allowed a single with two outs to Grossman, but worked out of the jam when he retired Jose Altuve.
NOTES: Houston Texans' first-round draft pick receiver DeAndre Hopkins threw out the ceremonial first pitch on Tuesday night. ... Former Astros star Larry Dierker was named special assistant to the president on Tuesday. Dierker, who made his debut for the Astros in 1964, will work as an ambassador for the team, handling speaking engagements and other fan events. ... The Astros, whose Triple-A affiliate is in Oklahoma City, announced plans to raise money through their foundation to help victims of Monday's devastating tornado in Oklahoma. They will hold a silent auction of game-worn jerseys and sell grab bags containing autographed baseballs. All of the proceeds will go to the American Red Cross relief efforts. "We have close ties to that community and many friends there," Houston president Reid Ryan said. "Those are the folks that support us in Oklahoma City, so we're eager to do our part to help them out in a time of need."