With two outs against Cincinnati in the top of the ninth and runners on first and second, Wright was called in to replace starter Brian Moehler to end the game.
It was a save situation, with the tying runner at the plate, after Moehler gave up a single and a walk.
But Wright seemed up to the task, looking unfazed as he struck out pinch-hitter Javier Valentin to end the game.
As it turned out, he did not even know the situation he was in.
"When I left the bullpen I wasn't thinking about that," he said. "I was just thinking, 'Let's get this out so we can get back to the clubhouse.' They told me [afterward] it was my first save. I was kind of excited because I really didn't know that was happening."
Astros manager Cecil Cooper said he had wanted to keep Moehler in for a complete game but that the situation was a perfect one for Wright. He liked the matchup of young guys against each other.
He was surprised Wright was unaware of the save situation. Most pitchers, he said, are paying close attention to that.
"A chance to go and get a big out for us, and he did," Cooper said. "He made some nice pitches. That's just a big moment for him, but he was chewing his gum and working it, doing his usual stuff."
Wright said the moment, in hindsight, is just another in what he hopes will be a long and successful career. His first career win came with two outs as well.
He made sure to keep the ball that struck out Valentin, and he plans to send it home to his family.
"I know my mom and dad are watching back in Alabama," he said, "so they'll get a kick out of it."
Krysten Oliphant is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.