Prado followed with a sharp grounder through the right side of the infield, sending the National League wild card-leading Braves to their second straight walk-off win.
They downed the Giants in Monday's first game of the series by rallying for three runs against closer Brian Wilson in the ninth.
Arodys Vizcaino (1-0) earned the victory for Atlanta.
San Francisco starter Jonathan Sanchez left the game in the third inning because of a left ankle sprain. He was replaced by Guillermo Mota.
The Giants' loss put them 3 1/2 games behind first-place Arizona in the National League West.