With the Twins down 2-1, Chris Parmelee and Trevor Plouffe opened the Minnesota fourth with singles on the first two pitches of the inning. Arcia, who had just one hit in his career, pulled the next pitch well beyond the right-field wall for a three-run home run.
That handed the loss to Jose Fernandez (0-2), who was changed with four runs and six hits in five innings.
Kevin Correia (2-1) gave up two runs and five hits while walking one and striking out five over seven innings but had to sweat out an eighth-inning Marlins' rally before getting the win.
Minnesota reliever Jared Burton allowed a single to Juan Pierre and then hit Placido Polanco and Giancarlo Stanton to load the bases. Greg Dobbs hit a line drive that went off Burton's glove but shortstop Pedro Florimon was able to reach and throw Dobbs out at first. A ground out then ended the threat.
Glen Perkins came in the ninth and posted three strikeouts for his sixth save.
Brian Dozier opened the Twins' first with a triple and scored on Justin Morneau's fielder's choice but Miami took the lead in the fourth with a two-run single by Joe Mahoney.
Poor weather -- cold and snow -- forced the postponement of Monday's game, which was rescheduled as a day-night doubleheader for Tuesday.
Celebrity Families of 2014 [PHOTOS]