Wood (2-2) allowed one run and two hits in his fourth major league start. The unorthodox 22-year-old rookie left-hander, who configures his body in an unusual way during his delivery, struck out three and walked two.
"(Braves catcher Brian McCann) and I had a good game plan, just attack and make good pitches," Wood said. "I didn't want to be the one who lost the streak."
Johnson, who entered leading the league in batting, hit a two-run single in the first to stake the Braves to an early lead. Justin Upton and B.J. Upton each had two hits with a double apiece for Atlanta, which matched its season-best winning streak.
"Our offense got us going," Wood said. "To get two runs before I got out there, you feel like you have a little room to work with."
Philadelphia managed just four hits while dropping its fifth straight and 13th in the last 14. The Phillies have just 33 runs in their last 14 outings.
The home fans voiced their displeasure several times during the evening, including greeting closer Jonathan Papelbon with boos when he entered in the ninth. Papelbon pitched a scoreless frame. The loudest boos were targeted at Delmon Young after he struck out for the fourth time in the ninth inning.
And the frustration appears to be seeping into the clubhouse, as well.
"You've got to show more hungriness when you're hitting," manager Charlie Manuel said. "I don't see no getting after at-bats. Looks like we take it very casual. We say, 'We'll get 'em next time.' No, that's not good enough.
"At times, we definitely get out-talented but that doesn't give you any reason why you can't concentrate, stay focused on your at-bats and play the game right."
Cliff Lee (10-5) matched his shortest outing of the season while continuing his recent struggles. The left-hander gave up four runs -- three earned -- on eight hits in five innings to lose for the third consecutive start. Lee, who last pitched on July 21 and had his last turn in the rotation skipped due to a stiff neck, has a 6.00 ERA during his losing streak.
Lee said the Phillies need to play with more energy.
"Not much you can find that's good about the way we've played the last couple of weeks," he said. "We're getting outplayed all the way around.
"We've got to have more pride, more fire and play better fundamental baseball. Period. If we do that, we'll turn it around."
The Braves, who surged to a 12½-game lead over Washington in the NL East, scored a pair of runs in the first inning on Johnson's two-run single. After the Phillies got a run back in the third on Michael Young's groundout, RBI hits by Jason Heyward and Justin Upton in the fourth pushed Atlanta's lead to 4-1. Upton's double extended his hitting streak to nine games.
Craig Kimbrel pitched a scoreless ninth for his NL-leading 34th save in 37 chances.
There were two reviews of called home runs that were overturned by replay.
Carlos Ruiz's third-inning double originally was ruled a home run by third-base umpire Gary Cederstrom but changed when replays showed the ball didn't clear the metal fence atop the wall in left field.
And B.J. Upton's fourth-inning double was called a homer but overturned after a lengthy delay when the umpires apparently determined that a fan interfered with the ball prior to it going over the wall.
A noticeably annoyed Lee stalked around the mound, slammed the ball into his glove and conversed with home-plate umpire Kerwin Danley during the delay.
"It doesn't help anything to delay the game for five, six, seven minutes, however long it takes to review it," Lee said. "There's got to be a better way to do it. I don't know what it is. On one hand they talk about the pace of the game, they need to speed the game up. Then they go to replays to get it right, but then that's slowing the game down. There's got to be a way to make it quicker."
The Braves also won 10 straight games from April 5-16. ... The Phillies have lost five straight series. ... Darin Ruf extended his streak to 32 straight games reaching base safely with a fourth-inning single. Ruf also singled in the ninth. ... After an off day on Monday, the Phillies host Chicago for a three-game series beginning at 7:05 Tuesday night when right-hander Kyle Kendrick (9-8, 4.29 ERA) opposes Cubs right-hander Edwin Jackson (7-11, 4.65). ... Braves lefty Mike Minor (11-5, 2.75) faces Nationals right-hander Stephen Strasburg (5-9, 3.04) at 7:05 Monday when the teams begin a three-game series in Washington.