Francisco's blast in the fourth inning capped a three-run rally that erased a 1-0 deficit and helped boost the Braves to a win in the rubber match of a three-game series with the Marlins.
The third baseman's RBI single in the sixth put Atlanta up 6-1 and the Braves also got solo homers from Michael Bourn and Jason Hayward in recording their fifth win in seven games overall.
Tommy Hanson (11-5) earned the victory despite issuing seven walks through five innings. The right-hander managed to hold Miami to one run on three hits, striking out seven.
Marlins starter Ricky Nolasco (8-9) was tagged for six runs on eight hits, lasting 5 1/3 frames.
Justin Ruggiano drove in the only run for Miami, which stole seven bases in the loss.