Glavine, who walked one and struck out four, finished the sixth by retiring his 17th straight batter. The lone blemish of the day came on an inside fastball that Luis Castillo drove into the left-field seats in the first inning.
"Five great innings of nothing and he really got it together and was throwing good," said Braves manager Bobby Cox.
Glavine (2-1, 3.98 ERA) admitted this weekend he always dreaded playing the Braves when he was in the visitors' dugout. And he won't deny it showed in the way he pitched.
Glavine compiled a 61-57 record in his five seasons in Flushing, but was 4-11 with a 5.15 ERA in 19 starts against Atlanta. He lost eight of his first nine starts against the Braves, including four straight to start 2003.
Even more difficult to stomach was his poor performance at Turner Field, where he was 3-7 with a 5.64 ERA in 12 starts.
But over the course of his career, Glavine has always pitched well against the Mets, and is now 17-7 with a 2.82 ERA against them.
"It's a different feeling pitching against a team that you were with for 16 years vs. a team you were with for five," Glavine said. "It was a little bit different than when I came back here and was pitching against all these guys for the first time."
Glavine is 2-0 in his last three starts, allowing 12 hits and seven earned runs in 18 2/3 innings.
"He made quality pitches when he had to," Braves catcher Brian McCann said. "He's the type of pitcher that once he settles down and gets a feel for what the hitters are doing, then he goes with a game plan."
Glavine needed just 82 pitches to retire the punchless Mets, and 26 of those came in a sloppy first inning. He didn't return after the sixth because of a nagging right knee injury that he said has bothered him for a couple of weeks.
"Today was the first it has bothered me and I don't know why," Glavine said.
After allowing a Ryan Church single in the first inning, Glavine and the Braves' bullpen combined to retire the next 22 batters. Jose Reyes broke that streak with a single off Blaine Boyer in the eighth.
"He's extremely creative and he changes speeds," said Mets third baseman David Wright, who said he will probably send Glavine a congratulatory text message after the second game. "It just goes to show you that you don't have to have overpowering stuff or throw 90 mph to win baseball games. He's been doing it his whole career, and it's a frustrating at-bat because he never gives in and gets you to chase pitches that are borderline balls and strikes."