"I tried to be as calm as possible and not get too worked up, and I think that helps me," the 22-year-old Zimmermann said. "I wasn't nervous at all. I just got up there and did my thing."
Tigers starter Edwin Jackson struck out three and walked one in two innings.
The Nationals broke the scoreless tie in the third inning when Wil Nieves doubled off Nate Robertson, driving in Pete Orr.
Detroit tied it in the fifth when Clete Thomas singled home Ryan Raburn. Washington scored in the bottom half as Chris Marrero doubled home Orr.
Mike O'Connor got the victory and Rick Porcello took the loss. Wil Ledezma and Jesus Colome finished up with a scoreless inning apiece for the Nationals.
Notes: The Nationals fired Jose Rijo, who had been a special assistant to general manager Jim Bowden. Rijo took a leave of absence over the weekend after a Major League Baseball investigation revealed a prospect he discovered was older than originally believed. Last week, it was announced that Esmailyn "Smiley" Gonzalez of the Dominican Republic lied about his age and name. The Nationals also cut ties with Rijo's training facility in the Dominican.