The Astros couldn't hang on to give Norris his fourth win of the season.
Alex Avila hit a two-run home run in the ninth inning off Astros closer Jose Veras, lifting the Tigers to a 4-3 victory.
Norris struck out a season-high seven in seven innings, allowing two runs and five hits.
The right-hander walked three, and kept the Astros in the game.
Norris said he was in a groove, and he and catcher Carlos Corporan had a great rapport.
"I went out there and executed some pitches," Norris said. "These guys played defense behind me. We came out with the short end of the stick, but these guys fought hard for nine innings, and that's what we expect out of ourselves.
"It's a tough one to lose, but we played hard, and that's a positive for us."
Houston manager Bo Porter praised Norris' work after the Astros fell to the Tigers in extra innings Thursday night.
"Bud Norris did what a No. 1 starter does when his team is light in the bullpen after playing a 14-inning game," Porter said. "He went out for seven innings and pitched like a No. 1 starter and held one of the best offensive teams in our league to two runs."
After Houston closer Jose Veras walked Don Kelly to open the ninth inning, Avila hit a 3-1 fastball to deep center field with one out and help the Tigers win their seventh game in eight tries.
"That's the game," said Veras (0-2), who has blown two saves in four opportunities.
"Sometimes things don't go your way. That is a hitter that has been hitting .160-something, .170 and .150 against the fastball. He hit a pitch down and away out of the ballpark. You can't say anything to it other than he made good contact."
Jose Altuve's RBI single in the seventh inning capped a three-run rally and gave the Astros a 3-2 lead.
Houston, which has the worst record in the American League, lost its fourth in a row and eighth in the past nine games.
Porter said he told his young team not to hang their heads because they played well.
"Losing is tough any time," Porter said. "At the same time, from last night's game to tonight's game, you take away that this is the defending American League champion, and one play here or one play there, we are going home victorious and 2-0 against the American League champion. Unfortunately, that didn't happen. They made plays."
Tigers left-hander Drew Smyly (2-0) pitched two scoreless innings for the win, and Jose Valverde finished the ninth against his former team for his third save.
Tigers starter Doug Fister, who had won his four previous decisions, pitched six innings of shutout ball, but things unraveled for the Tigers' right-hander in the seventh, with Detroit up 2-0.
Matt Dominguez doubled on a line drive to left to lead off the inning, and Rick Ankiel followed with a single to center that had Fister ducking and deflecting the ball with his glove.
Marvin Gonzalez reached on an error by second baseman Omar Infante, allowing Dominguez to score, and Ankiel scored the tying run on Robbie Grossman's RBI single to left.
That set the stage for Altuve, whose third hit of the night gave the Astros their short-lived lead and marked the end of Fister's outing.
Fister allowed three runs, two earned, and nine hits over six-plus innings. He struck out four while walking one. He was replaced by Smyly.
"That team is playing their (butts) off," Detroit manager Jim Leyland said. "They are good. They might be young in some areas, but they are playing their fannies off against us."
Leyland was impressed by Norris.
"That wasn't easy for us tonight," he said. "He pitched very, very well."
Jhonny Peralta gave the Tigers a 1-0 lead with an RBI single to left in the second inning.
Victor Martinez made it 2-0 with an RBI single to the right-field wall in the fourth. Martinez thought he had a home run. The play was reviewed by the umpiring crew, who upheld with the initial call.
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