Stanton belted a two-run shot in the first inning, drove in a game-tying run with a sixth-inning single and added a solo clout in the eighth for the Marlins, who salvaged one victory in their three-game home series.
Nick Green also went deep and Donovan Solano added a go-ahead RBI as the Marlins snapped a six-game losing streak.
Ricky Nolasco (2-2) allowed three runs on four hits over seven innings to notch the win, striking out two and walking two.
Steve Cishek yielded a run in the ninth but hung on for his third save.
Cubs starter Carlos Villanueva (1-1) was touched for four runs on four hits over six full frames. He struck out eight.
Dioner Navarro homered and Starling Castro went 2-for-4 with a two-run double for Chicago.