The 40-year-old Jones had two hits and is batting .316 in his final season before retirement.
The Braves, 6-1 on their 10-game homestand, remained 2½ games behind first-place Washington in the NL East. They won three times in the four-game series.
Miami’s Jose Reyes led off the sixth with a triple to left field, giving him a 20-game hitting streak to match his career high.
Reyes scored on Carlos Lee’s sacrifice fly.
Jason Heyward had three hits and drove in a run for Atlanta.
Braves starter Mike Minor gave up two hits in 3⅔ scoreless innings but didn’t return following a rain delay of 42 minutes.
Cristhian Martinez (5-2) took over for Minor when play resumed in the fourth. Martinez allowed four hits and one run in three innings.
Braves closer Craig Kimbrel stranded two runners in the ninth, striking out Emilio Bonifacio to end the game.
Making his second start since coming to Miami in the trade that sent Hanley Ramirez to the Dodgers, Nathan Eovaldi (2-7) gave up six runs and eight hits with one walk and one hit batter in two innings. It was the shortest of his 18 career starts.
Eovaldi yielded only one run over 5⅓ innings in a 4-2 win over San Diego in his Marlins debut Saturday.
Chad Gaudin followed Eovaldi with four scoreless innings, allowing one hit and one walk.
The Braves sent nine batters to the plate in their three-run first inning. Following singles by Reed Johnson and Heyward, Jones hit a two-run double and scored on Dan Uggla’s single.
Eovaldi gave up three more runs in the second. The right-hander hit Johnson with a pitch after giving up a single to Michael Bourn. Heyward drove in Bourn with a single to left and Freeman added a two-run double to right.
The Marlins had a depleted bench for the game.
Third baseman Donnie Murphy was scratched from the starting lineup with flu-like symptoms. Outfielder Bryan Petersen was held out with a sore right shoulder he hurt while diving for a ball in Wednesday night’s game. Outfielder Justin Ruggiano was held out with back spasms.
Petersen walked as a pinch-hitter in the ninth.
Gorkys Hernandez, acquired from the Pirates on Tuesday, was 0 for 4 in his first start for Miami in center field.
Marlins left-hander Dan Jennings loaded the bases in the eighth on two walks and a hit batter.
Jennings escaped the jam but limped off the field after covering first base on Heyward’s inning-ending grounder to first.
NOTES: Reyes also had a 20-game hitting streak in 2005 with the Mets. ... Johnson made his second straight start for the Braves, this time in left field, following his trade from Chicago this week. Martin Prado, only 6 for 28 (.214) in the first six games of the homestand, was given a day off. ... The Marlins will call up LHP Brad Hand from Triple-A New Orleans to pitch the first game of Friday’s doubleheader at Washington. RHP Josh Johnson will start the second game. ... The Braves open a series against the Astros when RHP Tim Hudson faces Houston RHP Armando Galarraga on Friday night.