The Phillies have won two in a row after losing nine of 10.
Blanton (6-6) struck out seven and did not walk a batter while throwing 111 pitches. He has eight complete games in his career, but the two he has thrown this season have been his first since 2007.
The only run Blanton allowed came on a homer by Trevor Plouffe in the second that forged a 1-1 tie.
Jim Thome snapped that tie in the third with a three-run blast off starter Scott Diamond (5-2). Carlos Ruiz added an RBI double in the eighth and Placido Polanco drove in a run with a single in the ninth.
Diamond gave up four runs on five hits in six innings.