Blanton (4-3) shook off a persistent rain to tame the Astros on one run, surrendering six hits while issuing only one walk and striking out seven.
Galvin's RBI single in the fifth inning broke a scoreless tie and put the Phillies ahead for good. The rookie second baseman added another run-scoring single in the next frame for a 3-0 lead.
Placido Polanco added a two-run homer for Philadelphia, which claimed the first of a two-game set at Citizens Bank Park.
Houston's Lucas Harrell (2-3) absorbed the loss despite allowing only two runs on five hits over 5 2/3 innings.
Marwin Gonzalez collected his first major league homer for the Astros, who lost for the sixth time in eight games.