ATLANTA — The Florida Marlins rarely win a series in Atlanta, so manager Fredi Gonzalez wasn’t about to let this one get away.

    Aaron Boone homered for the second day in a row, the Florida bullpen kept the Braves from rallying and the Marlins held on for a 7-4 victory Thursday.

    Florida built a 5-0 lead by the third inning, capped by Boone’s two-run shot, and took no chances when starter Scott Olsen struggled with his control.

    Olsen was yanked in the fifth after giving up a two-run single to Jeff Francoeur, having walked five in 4 1-3 innings. He left with a 5-2 lead, but didn’t pitch long enough to qualify for the win.

    ‘‘You owe it to the other 24 guys,’’ Gonzalez said. ‘‘You would love to have given him the opportunity, but it was one of those gut feelings, you know?’’

    Justin Miller got out of further trouble in the fifth and Kevin Gregg escaped a bases-loaded jam in the eighth.

    Olsen was tightlipped about being yanked just two outs short of qualifying for a win.

    ‘‘Not my call,’’ he kept repeating over and over, though he did concede, ‘‘My control was bad on every ball I threw, for the most part.’’

    Gonzalez wasn’t concerned about shaking Olsen’s confidence.

    ‘‘We’ll keep building on it,’’ the manager said. ‘‘Here’s a 23-year old kid that we need to get better. We will and he will.’’

    Florida took three of four at Turner Field, only its second series win in Atlanta since 2002. The Braves have lost four of five, costing them a chance to climb closer to first-place New York in the NL East.

    Justin Miller (1-0) worked 1 2-3 scoreless innings for the win. Gregg finished up his ninth save in as many chances.

    The Marlins jumped on Kyle Davies (3-4) right away. Alfredo Amezaga and Dan Uggla started the game with singles and Josh Willingham drove them both home with a double to the gap in left-center.

    Florida made it 5-0 in the third. Uggla led off with a double, stole third and wound up scoring on Jeremy Hermida’s sacrifice fly.

    Davies, who had walked Willingham, squandered a chance to escape further damage when he hung a slider to Boone with two outs. The first baseman drove it into the left-field seats, his fifth homer of the season and second in three games.

    ‘‘It’s important to score runs, whether it’s early or late,’’ said Boone, who also homered in the opener of Tuesday’s doubleheader.

    Davies steadied himself after a rough April but is still looking for some sort of consistency. He lasted only five innings. He gave up five runs on six hits and two walks.

    ‘‘If it’s 3-0, the game is a little more interesting,’’ Davies said. ‘‘But I hang a slider, the ball is gone and it’s 5-0. That’s a big difference.’’

    In five of his starts, the 23-year-old right-hander has averaged just over seven innings, going 3-0 with an ERA of 2.29. In his other six appearances, he’s not lasted more than 5 1-3 innings, going 0-4 with a 9.22 ERA. ‘‘The aggressiveness has got to be there,’’ Davies said.

    ‘‘That’s what I’m going to work on so I can get on a roll. I’m tired of this roller coaster. Up and down. Up and down.’’

    Down 7-2, Atlanta tried to rally in the eighth. Kelly Johnson hit a two-out, two-run single off Taylor Tankersley and the Braves loaded the bases.

    But Gregg retired Francoeur on a weak grounder to third, then breezed through the ninth.

    The Braves, who have struggled offensively, left 12 runners on base, and Francoeur was easily thrown out at second when he tried foolishly tried to stretch a single into a double with Atlanta down 5-0.

    ‘‘If we had been doing better, he’s probably not running there,’’ teammate Scott Thorman said. ‘‘Everybody is trying do too much.’’