Bumgarner (4-1) yielded one run on four hits, walking two in notching his first victory since April 13.
Blanco went 2-for-2 with four RBI, including a bases-clearing double and an RBI triple. Pablo Sandoval smacked a solo homer for the Giants.
Brandon Belt supplied a two-run single to cap the scoring in the eighth as San Francisco evened its three-game series.
Braves starter Paul Maholm (4-4) was tagged for six runs on eight hits over 4 1/3 frames.
Maholm also provided Atlanta's only RBI with a fifth-inning single.