Ross's three-run shot in the fourth inning broke a scoreless tie and his two-run bomb in the fifth made it 7-4 for the Bosox, who claimed the rubber match of their three-game interleague set at Fenway Park.
Aaron Cook (1-1) logged the victory after being activated for the start following a knee injury. He took the rotation spot of Clay Buchholz, who was put on the disabled list with a gastrointestinal illness.
Cook responded by holding the Braves to three runs (two earned) on six hits over five frames.
Braves starter Mike Minor (3-6), meanwhile, was roughed up for seven runs (four earned) on six hits in a 4 2/3-inning effort.