Hanson (13-9) allowed two runs, one earned, and six hits in 5 1-3 innings for his first win since July 30, also against Miami. The right-hander was 0-4 with a 5.06 ERA in his previous seven starts.
Miami led 2-0 before the Braves scored four runs in the fourth inning. Dan Uggla and Simmons had run-scoring doubles before Jacob Turner (1-4) walked Jose Constanza to load the bases.
Petersen dropped Martin Prado’s sinking liner, allowing Ross and Simmons to score.
The Braves, who have clinched at least a wild-card berth, have won five in a row. They began the night four games behind Washington in the NL East.
Atlanta swept the three-game series to finish 14-4 against the Marlins for the season.
Miami has lost seven straight for its longest slide of a disappointing year.
The Braves extended their lead with two runs in the seventh. Wade LeBlanc gave up a double to Prado before loading the bases with walks to Jason Heyward and Freddie Freeman. Uggla hit a two-run single off Ryan Webb.
Atlanta’s Chipper Jones, continuing the final homestand of his career, tipped his helmet when fans rose for a standing ovation before his first at-bat in the second. Jones then took a deep breath, entered the batter’s box and drew a walk. He was 0 for 3.
Jones, 40, is retiring after the season and will be honored by the team before Friday night’s game against the Mets.
Turner allowed four runs, two earned, and six hits in six innings.
Petersen hit a leadoff double in the third and scored on Carlos Lee’s two-out double down the left-field line.
The Marlins added a run in the fourth. Scott Cousins singled, moved to second on Hanson’s wild pickoff throw, and scored on a double by Gil Velazquez.
NOTES: Braves CF Michael Bourn (jammed left thumb) missed his fourth straight start. An MRI showed no tear. The Braves say Bourn is day to day with a slight sprain. ... Braves C Brian McCann was held out with a sore right knee. “He’s just having a tough time moving around back there,” manager Fredi Gonzalez said. ... Atlanta’s Tim Hudson (16-6) will face LHP Jonathon Niese as the Braves open a weekend series against the Mets on Friday night. After the series, the Braves close the regular season with three games at Pittsburgh. ... The Marlins return to Miami to open a series against Philadelphia. Miami LHP Mark Buehrle (13-13) will face Cliff Lee (6-8).