After the Mets spent all afternoon answering questions about the future of manager Art Howe, they came back from a three-run deficit to win for only the third time in 22 games.
Drew and Adam LaRoche each hit a two-out, two-run double during Atlanta's four-run third inning in the nightcap. Jae Seo (4-10) allowed five runs and seven hits in four innings, dropping to 0-5 in nine outings since beating Cincinnati 7-5 on June 29.
Rafael Furcal hit a sacrifice fly in the fourth, Drew had an RBI single in the seventh off Heath Bell and Eli Marrero added a sacrifice fly in the ninth.
That was plenty for Byrd (7-5), who shrugged off Mike Cameron's leadoff homer in the first. He allowed seven hits, struck out four and walked none to win for the third time in four starts. The right-hander also improved to 8-1 in 13 lifetime appearances against his former team, including 11 starts.
Drew went 6-for-9 with four RBIs in the doubleheader, and LaRoche was 4-for-7.
The NL East-leading Braves sent the free-falling Mets to their 20th loss in 23 games.
In the opener, Andruw Jones hit a two-run homer, but Jaret Wright (14-7) couldn't hold the lead, as New York scored five times in the sixth.
Aaron Heilman (1-1) earned his first major league win in more than a year, and Wilson Delgado also homered.
Reds 4, Phillies 3
In Cincinnati, Jason LaRue drove in the go-ahead run on a fielder's choice grounder in the eighth inning and Cincinnati snapped Philadelphia's six-game winning streak.
Wily Mo Pena led off the eighth against reliever Felix Rodriguez (5-8) with a double into the right-center field gap and moved to third on a sacrifice.
Other results: Cubs 7, Pirates 2; Rockies 9, Diamondbacks 2; Padres 9, Dodgers 7.
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