Cantu broke a 3-3 tie with an RBI double and Paulino followed it up with a two-run single off Brewers reliever Trevor Hoffman (1-4), who continued a string of disastrous outings for Milwaukee.
Chris Coughlin socked a solo homer among his three hits for the Marlins.
The Florida rally made a winner of Ricky Nolasco (5-4), who yielded three runs on seven hits, one walk and eight strikeouts over seven innings. Leo Nunez nailed down the Marlins' third straight victory with his 11th save.
Corey Hart connected for a two-run homer and Prince Fielder added a solo shot in the Brewers' loss.
2014: The Year in Music [PHOTOS]