Wood (2-2) allowed one run, walked two and struck out three in his fourth major-league start, throwing 57-of-95 pitches for strikes.
Luis Avilan and Scott Downs combined for two scoreless relief innings and Craig Kimbrel finished up with his 34th save as the National League East-leading Braves swept a three-game series and improved to 67-45.
Chris Johnson opened the scoring with a two-run single in the first inning and Atlanta never trailed.
Cliff Lee (10-5) coughed up four runs (three earned) on eight hits over five full innings for the Phillies, who fell for the 13th time in 14 games.
Michael Young supplied Philadelphia's only RBI.