With a healthy Gattis, the Braves often relied on homers. Without the power-hitting catcher, they showed the Mets they can create runs without the long ball.
The Braves stole three bases, leading to two runs. They had only one extra-base hit, a run-scoring double by Freddie Freeman in the third inning.
''It's nice to play small ball, stealing bases and running the bases good, going first to third,'' Simmons said.
Gattis was placed on the 15-day disabled list before the game with a bulging disk in his back. He was tied for the team lead with 16 homers.
The Braves overcame a shaky start from Mike Minor to protect their one-half game lead over Washington in the NL East. Atlanta has won six straight, its longest streak of the season.
Shae Simmons (1-0) took over for Minor in the fifth and pitched 1 2/3 scoreless innings. Craig Kimbrel earned his 26th save by striking out Eric Young Jr., Granderson and Bobby Abreu in the ninth. Four Braves relievers combined to allow only one hit in 4 2/3 scoreless innings.
''I think the MVP of the team today was the bullpen,'' said Braves manager Fredi Gonzalez. ''To go 4 2/3 scoreless innings in a one-run game, that's a pretty awesome night for us down there.''
Matsuzaka (3-3) allowed five runs on seven hits and three walks in five innings. He has lost three straight starts.
With the game tied 2-2 in the fourth, the Braves staged an improbable three-run inning. Chris Johnson reached on only his eighth walk of the season. With two outs, Johnson scored from second on Minor's single to center - only his second RBI of the season. Following a single and stolen base by B.J. Upton, Andrelton Simmons' two-run single to left off Matsuzaka increased Atlanta's lead to 5-2.
''When they needed a big hit, they got it,'' said Mets manager Terry Collins of the Braves.
''There's a reason why they're winning. There's a reason why they've won. They do have a knack for it. Those are the kind of players they have over there. They're tough in the clutch, boy, they're very tough.''
Matsuzaka said it was disappointing to allow the three runs with two outs.
''The first two outs came pretty easily but I just wasn't able to finish off that inning with the last out,'' Matsuzaka said through a translator. ''... I was really disappointed in myself for not being able to keep us in the game.''
Minor quickly gave back two runs in the fifth on Murphy's two-run homer. Minor then gave up singles to Eric Campbell and Lucas Duda before being bailed out by rookie Shae Simmons, whose sidearm delivery produced a fly ball from Chris Young and a strikeout of Travis d'Arnaud.
Minor lasted 4 1-3 innings, matching his shortest start of the season, and allowed four runs on nine hits and one walk. His ERA is 4.73 and he has made eight starts since his last win on May 19.
Atlanta rookie catcher Christian Bethancourt, making his second straight start, singled in the second inning to drive in Johnson for his first career RBI.
Braves second baseman Tommy La Stella suffered a bruised right foot when he was hit by a pitch in the second inning. He left the game in the eighth. La Stella said he expects to play on Wednesday. Gonzalez said the rookie had a 50-50 chance to start.
A few hundred fans arrived early to watch the United States lose to Belgium in the World Cup. The game was shown on the stadium video board. ... Tejada has a 10-game hitting streak. ... B.J. Upton has an eight-game hitting streak and 13 stolen bases. He stole 12 bases in 2013. ... Gov. Nathan Deal threw out the first pitch. ... The Braves recalled RHP Juan Jaime from Triple-A Gwinnett and then optioned him back to Gwinnett after the game. RHP David Carpenter (strained right biceps) will come off the 15-day DL on Wednesday. ... The series ends Wednesday night with Atlanta's Julio Teheran facing New York's Jacob deGrom.