The Braves weren't able to dent Dodgers starter Chris Capuano for a run over seven innings, but trailing 1-0 in the eighth they erupted to take the lead.
B.J. Upton singled with one out, chasing Capuano, and Kenley Jansen (1-2) came in to pitch.
Gattis greeted him by pounding a pitch deep into the left field bleachers for the go-ahead blow, and Simmons followed with a solo shot as the Braves clinched their three-game series.
Cory Gearrin (1-0) earned the decision with a scoreless eighth inning following a strong start by Kris Medlen, who allowed only one unearned run on two hits over seven frames.
Craig Kimbrel notched his 13th save with a 1-2-3 ninth.
Capuano held Atlanta to one run on five hits over 7 1/3 innings, walking none while striking out five.