Atlanta then wasted a chance in the 10th by leaving the bases loaded, and San Diego finally came through in the 12th against Kris Medlen (3-4).
Hundley opened the inning with a double and, after Tony Gwynn struck out, Luis Rodriguez drew a walk.
Evereth Cabrera struck out to give the Braves a chance to escape the inning, but Eckstein doubled on Medlen's first pitch.
That made a winner out of Joe Thatcher (1-0), who was called up from Class AAA after San Diego placed Edgar Gonzalez on the disabled list with a concussion. It was the third career major league win for Thatcher, who worked 1 1/3 innings.
Edward Mujica turned in a perfect bottom of the 12th for his second save.