Blanton (3-3) did not walk a batter and had six strikeouts in his third career shutout, his first since June 2, 2007 for Oakland against Minnesota.
The Braves' only hits were singles by Freddie Freeman in the first, David Ross in the fifth and Michael Bourn in the ninth. Martin Prado then lined out into a double play to end the game.
Laynce Nix had two hits, including a homer, for the Phillies.
The game, which was played in 2 hours and 2 minutes, was a dramatic reversal of the Braves' 15-13 win in 11 innings on Wednesday night when the teams combined for 36 hits.