Minor (3-2), who outdueled Tim Lincecum, scattered four hits and struck out nine batters over six innings. Eric O`Flaherty pitched the seventh, Jonny Venters retired the side in order in the eighth and Craig Kimbrel notched his 37th save to set the National League rookie record.
Kimbrel, who had been tied with Todd Worrell (St. Louis, 1986), fanned the final two hitters. He also got great defense behind him when second baseman Dan Uggla made a tumbling over-the-shoulder catch in right-center field to rob Orlando Cabrera of a hit.
Thursday's 1-0 win allowed the Braves to widen their lead in the NL wild card standings to six games over the Giants.
Lincecum (11-10) fanned seven over as many innings and allowed five hits, but the Giants lost three of the four games in this series - each time by a run.