Ryan Howard had three hits with a double and an RBI for the Phillies, who are a major league-best 12-2 since the All-Star break.
Maikel Franco had two doubles and two RBIs, Herrera had three hits and Cesar Hernandez and Galvis each had two as the Phillies pounded out 15 hits.
Nick Markakis homered for Atlanta, which has lost a season-high six straight — all on the road. The Braves have dropped 13 of their last 14 away from Turner Field, and nine of their last 10 overall.
Aaron Nola (2-1) allowed two runs and five hits with three strikeouts and no walks.
Matt Wisler (5-2) gave up seven runs and eight hits in 4 2/3 innings.