Clark's 10th home run of the season came on a 2-2 pitch from Wilfredo Ledezma (0-2) and made amends for the Diamondbacks blowing a seven-run lead in regulation.
Edgar Gonzalez (4-2) was perfect in two innings of relief for Arizona.
The Braves did not go quietly. After giving up six runs in the second inning -- which was keyed by home runs by Eric Byrnes and Stephen Drew -- Atlanta scored twice in the fifth and four times in the sixth to cut the deficit to 7-6.
With two out in the ninth, Willie Harris drove in Yunel Escobar from second with a bloop single that tied the game and sent it into extra innings.