The Twins took an early 3-1 lead, fell behind in the fifth and then rallied in the seventh with a big inning against three Los Angeles hurlers.
Chris Parmelee promptly tripled in two runs to tie it up and LaTroy Hawkins relieved Takahashi (0-1). After Hawkins retired two batters, Carroll singled to right to bring home Parmelee with the winning run.
Jeff Gray (1-0), who threw only one pitch in relief of Carl Pavano in the seventh, was credited with the win. Matt Capps gave up a one-out double in the ninth, but collected his first save.
The Twins were the last team in the majors to record a victory, having lost their first four outings of the season.