Casey Kotchman homered and hit an RBI double for Atlanta. David Ross had a two-run homer.
Jurrjens (3-2) allowed two runs, both on homers by Hanley Ramirez. The right-hander's ERA rose to 2.01.
Marlins starter Anibal Sanchez (1-4) allowed two homers and four runs in 4 2-3 innings before leaving the game because of discomfort in his pitching shoulder. Sanchez underwent surgery on the shoulder in June 2007 and returned last July.
Florida extended a club-record streak of 20 consecutive games without a win by a starting pitcher. During that span the starters are 0-10. The last Marlins starter to win was Sanchez against Atlanta on April 16.
The Marlins lost their third consecutive game to finish a 1-3 homestand, during which they fell out of the lead in the NL East for the first time this season. They're 4-13 since an 11-1 start.
For the Braves, the sweep came at the start of an eight-game trip. They were swept at home by Florida for the first time ever April 14-16.
Atlanta took a 2-1 lead in the second when Kelly Johnson led off with a single and Ross hit his third homer. Kotchman hit his first homer in the third, and hit Sanchez's final pitch for a two-out RBI double in the fifth.
Rafael Soriano struck out Ramirez with two on to end the eighth inning, and Mike Gonzalez completed the four-hitter with a perfect ninth for his fifth save in six chances.
A disputed call cost the Marlins a run in the first inning. Emilio Bonifacio was called out trying to steal second, although TV replays showed he appeared to be safe. Ramirez homered on the next pitch.
That was Florida's last hit until Ramirez hit a two-out homer in the sixth, his fifth this season.
Notes: With runners in scoring position, Atlanta went 0 for 5 and Florida went 0 for 3. ... Braves 3B Chipper Jones was given the day off. ... Ramirez's multihomer game was his ninth. ... The Braves' bullpen has allowed only two homers this season.