The win helped the Astros, who had lost to Detroit the first five times that played this season, avoid a season sweep. It was also Houston's first win in Detroit since 2000 when the Astros were in the National League.
J.D. Martinez walked to lead off the Houston ninth and was lifted for pinch-runner Brandon Barnes. Corporan greeted reliever Phil Cole with a double that chased Barnes home. Trevor Crowe ran for Corporan and scored on a sacrifice fly for the final run.
The Tigers loaded the bases in the bottom of the ninth and Miguel Cabrera hit a drive that Barnes caught at the wall for the final out. That locked the win for Hector Ambriz (1-2), who got one out in the eighth. Jose Veras, despite two walks and a hit batter, got his fifth save.
Al Albuquerque (0-1) walked Martinez -- the only batter he faced -- and took the loss.
Corporan hit a second-inning home run but the Tigers, with Avisail Garcia hitting a three-run home run for his first major league homer, scored four times in the bottom of the inning.
Martinez had a three-run home run for Houston in a four-run fourth inning rally. Detroit tied the score with Matt Tuiasosopo's RBI single in the sixth.