Brantly's two-run double in the first inning put the Marlins ahead 3-0 and Miami was never headed en route to a split of its interleague doubleheader at frigid Target Field.
Giancarlo Stanton provided two hits and a pair of RBI while Justin Ruggiano and Chris Valaika each drove in a run as the Marlins broke a three-game skid and evened their three-game road set.
Ricky Nolasco (1-2) corralled his first win of the season, yielding three runs (two earned) on six hits over five full frames.
Steve Cishek hurled a scoreless ninth for his second save.
Twins starter Mike Pelfrey (2-2) was tagged for five runs on nine hits in a 4 2/3-inning effort.
Eduardo Escobar went 3-for-3 with two runs scored and Joe Mauer added two hits, including an RBI single, as Minnesota saw its five-game winning streak snapped.