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Matt Diaz and Eric Hinske also homered for the Braves, who scored six runs in the second and snapped a four-game losing streak, their longest since April. They maintained a two-game lead in the NL East over Philadelphia, which won 3-1 at San Diego.
The Braves built a 10-1 lead in the fourth -- the same advantage they had in last Wednesday's game at Colorado. Atlanta wound up losing that one 12-10, then got hammered 7-1 by the Marlins to open the weekend series.
Hudson (15-5) turned things around with an uncharacteristic performance by a sinkerballer who relies on ground balls for outs.
"I don't try to make guys miss the ball," said Hudson, who has come back from major elbow surgery with perhaps the best season of his career. "It was one of those nights where I had my swing-and-miss ball working. It was fun. Don't expect that out of me every night."
He struck out the first two Florida hitters to prevent a repeat of Friday night's debacle, when Tommy Hanson served up back-to-back homers to start the game. Those first two Ks gave Hudson 1,500 for his career, earning a long cheer from the Turner Field crowd.
He stepped off the mound, tipped his hat and smiled as the milestone was noted on the giant videoboard behind him.
"It's definitely something I'm proud of," Hudson said. "But it's definitely not something I'm known for."
It was on this night. Hudson closed with a flourish, fanning the side in the seventh to eclipse his previous career best of 12 strikeouts.
Florida went down swinging all but once against Hudson, who has put up double-digits Ks only 11 times in 337 career starts. His previous season high was seven.
"His sinker is dirty," Florida's Chad Tracy said. "You think you're on it, and then you aren't."
The Braves blew this one open early, sending 11 hitters to the plate in the second against Ricky Nolasco (14-9). Prado had a bases-loaded walk to account for his first RBI of the night. He added a two-run single in the third and a two-run homer in the seventh, equaling the five RBI he had at Milwaukee on May 10.
Prado is playing with a broken right pinky, but it's hard to tell.
"I'm trying to find the best way to swing the bat," said Prado, who was holding his finger in a cup of ice water after the game. "I guess I'm going to have good days and bad days. I had one of those good nights. Even better, we got the win."
Diaz, making a rare start against a right-handed pitcher, led off the second with a homer to center. Alex Gonzalez beat out an infield hit, Melky Cabrera singled and Hudson bunted them over to second and third.
Another infield hit, this one on a grounder to shortstop by Omar Infante, made it 2-0. Jason Heyward ripped a grounder off the chest of first baseman Gaby Sanchez, which was ruled the third infield hit of the inning and loaded the bases. After Prado's walk, Brian McCann cleared the bases with a three-run double into the right-field corner to make it 6-0.
Nolasco was replaced at the start of the third, having allowed seven hits and three walks in his shortest start of the season. He had skipped his previous turn because of a torn meniscus in his right knee, but said he felt fine and that had nothing to do with his dismal outing.
"I didn't throw anything where I wanted to," Nolasco said. "I didn't have it tonight. There's not much you can do. I'm not making any excuses. I just didn't do the job."
The Marlins also played some shoddy defense, even though they were charged with only one error. In addition to the liner off Sanchez, McCann picked up a gift single when shortstop Hanley Ramirez couldn't find a popup in short left. Ramirez did recover in time to throw out Prado, trying to score all the way from first.
Florida's only statistical error came on another popup into short left. Again, Ramirez drifted back and appeared to have this one well in hand -- until Logan Morrison charged in and knocked it out of his teammate's glove. Diaz scored on the miscue, avoiding a swipe tag by wisely choosing not to slide.
After replacing Derrek Lee at first base, Hinske led off the fourth with a homer.
- Lee has a strained right side and was removed for precautionary reasons. Braves manager Bobby Cox said he might hold Lee out of Sunday's game just to make sure he's OK.
- Florida OF Cameron Maybin was back in the lineup after coming out the previous night with what was announced as a strained groin. Maybin said he was merely dehydrated.
- The Marlins lost for only the third time in 11 games.