Kelly (1-0), a 22-year-old former first-round draft choice of the Boston Red Sox, didn't allow a runner to reach third base, scattering three hits while walking two and recording four strikeouts.
Tommy Layne and Dale Thayer followed with one scoreless frame each and Luke Gregerson picked up his second save for San Diego, which took the opener of the three-game series.
Yasmani Grandal provided all of the Padres' offense with a two-run homer and a run-scoring single.
Braves starter Paul Maholm (11-9) absorbed the loss, surrendering a pair of runs on eight hits over 6 2/3 innings. The left-hander walked one and struck out five for National League wild card-leading Atlanta.