Uggla had been 0 for 24 against the knuckleballer before his home run capped a four-run third and gave Atlanta a 6-3 lead. His bigger concern was his lack of home runs in his first 11 games.
"It's a huge load off your shoulders, especially when you're kind of known for being a power hitter," Uggla said. "It was tough for me to shoulder. I was having dreams about it."
Francisco homered in the second and Freeman hit an opposite-field drive to left in the fifth, his first of the season. That chased Dickey (2-1), who allowed eight runs and eight hits in 4 1/3 innings in his worst outing in four years.
There was light rain through the early innings, making it more difficult for Dickey to deliver his specialty pitch.
"It's like throwing water balloons," Dickey said. "That can't be an excuse. I still have to find a way to keep us in the ball game. Today I didn't give us a very good chance."
Mets manager Terry Collins said the wet weather "certainly had a huge effect."
"You've got to have a good grip on it and in the constant rain, it was really hard for him to throw," Collins said.
Atlanta has won seven of eight since opening the season with four losses, including three straight in New York. The Braves set season highs for runs and hits (16). They scored 43 runs in going 5-1 on the homestand.
"Today's game, we just kept adding on," Braves manager Fredi Gonzalez said. "I thought it was one of those games where if you didn't, you'd be up against it. ... We've got the guys who are capable of doing it."
David Wright had three RBIs, tying Darryl Strawberry for the Mets' career record at 733. Ike Davis homered for New York, which completed a 3-3 trip. The Mets won the series opener before two straight lopsided losses.
"You'll take .500 on the road, but because we got started on the trip so well, it's a little disappointing the way it ended the last two days," Collins said.
Cristhian Martinez (1-0) gave up one run and three hits in two innings to win in relief of Jair Jurrjens, whose ERA rose to 8.10. Winless in three starts, Jurrjens allowed four runs, seven hits and four walks in four-plus innings.
Trailing 3-2, the Braves went ahead in the third on Martin Prado's two-run double. After Uggla's homer extended the lead, the Mets closed to 6-4 in the fifth on a run-scoring infield hit by Wright.
Freeman's homer made it 8-4 in the bottom half. New Mets leadoff hitter Kirk Nieuwenhuis, who had three hits and scored three runs, had an RBI single in a run in the sixth.
New York's Josh Thole has reached base safely in all 11 games he has played. ... Atlanta has won three straight series. ... Dickey's streak of 14 straight quality starts ended. He had not allowed eight runs since Aug. 8, 2008, for Seattle against the Chicago White Sox. ... Braves RHP Chad Durbin struck out pinch-hitter Scott Hairston to end the seventh with the bases loaded. ... Bo Jackson threw out the ceremonial first pitch to promote his "Bo Bikes Bama" 300-mile bicycle ride on April 24-28 to raise money for areas in Alabama damaged by deadly tornadoes last year. ... The Braves open a four-game series at Arizona on Thursday night as LHP Mike Minor looks for his second straight win against the Diamondbacks' Josh Collmenter. ... The Mets, off on Thursday, open a four-game home series against the Giants on Friday with Barry Zito scheduled to face Jonathon Niese in a matchup of left-handers.