"We had nine hits," said manager Fredi Gonzalez, whose team went 0-for-6 with runners in scoring position and left 10 men on base. "We just have to get that next hit."
Gavin Floyd grinded through most of his five innings of work in his fifth start. The right-hander allowed six hits and three walks, and he limited Boston to just one earned run and stranded six baserunners on 106 pitches.
John Lackey was strong opposite Floyd, fanning nine and scattering eight hits without surrendering a walk or a run in 6 1/3 scoreless innings to improve to 6-3 while Floyd fell to 0-2.
The Braves did have an opportunity to charge some runs to Lackey when he exited with two on and one out in the seventh, but Chris Capuano eventually got Freddie Freeman to ground out to second with the bases loaded to keep Atlanta off the board.
Entering Wednesday night, Freeman was batting .326 with a .896 OPS and 17 RBIs with runners in scoring position this season. Atlanta is just 6-for-33 with runners in scoring position in its past five games, and five of those hits came on Monday.
"We had some people in the right situations," Gonzalez said. "We just couldn't break through."
Already clinging to a two-run lead in the sixth, Boston added a run off Alex Wood, who came on for Floyd, when Jackie Bradley Jr. doubled to left to score Jonny Gomes. Wood forced a groundout and then struck out Xander Bogaerts with two on to limit the damage.
Wood got into some more trouble in the seventh, and he almost escaped unscathed again. Gomes singled home Dustin Pedroia with one out, but Ryan Lavarnway grounded into a double play with one out and the bases loaded. After two consecutive scoreless appearances, Wood allowed five hits, two walks and two runs over 2 2/3 innings Wednesday.
The Red Sox struck first in the second inning when Daniel Nava grounded into a 4-6-3 double play, allowing Gomes to score. Floyd stranded a pair of runners in the first inning to keep Boston off the board early.
"You try to hope things turn around and try to keep on battling out there," Floyd said of the first inning. "It seemed today, just a couple things didn't go our way."
Boston then added to its lead in the third with an RBI single by A.J. Pierzynski to score Bogaerts, who reached second on a sky-high popup that fell in between center fielder B.J. Upton and shortstop Ramiro Pena. David Ortiz kept the inning alive by legging out a single that Braves' second baseman Tommy La Stella knocked down in the shift. La Stella, Atlanta's No. 7 prospect, had a pair of singles in his Major League debut after getting the callup Wednesday morning.
"I wish I would have done a better job enjoying it," La Stella said. "I was pretty focused on the game, but hopefully I get to enjoy it a little bit tonight with my family."
The Braves got just one runner to third Wednesday night, thanks to Lackey's strong command and swing-and-miss stuff.
Justin Upton came close to cutting a two-run Boston lead in half in the sixth, but his high fly ball clipped the top of the Green Monster in left for a double.
"There's been a number of starts where he's not walked people. He's had a very good fastball with some swing and miss," Red Sox manager John Farrell said of Lackey. "Another shutout here tonight. Just a high number of strikes. Was able to get a strikeout in some key spots, particularly to Upton. He set the tone here tonight."
Junichi Tazawa pitched a 1-2-3 eighth inning for the Red Sox, striking out two. Craig Breslow worked a scoreless ninth.