Aviles also stroked a run-scoring single to finish with four RBI while Darnell McDonald went 3-for-4 with a two-run homer and three runs scored for the Bosox, who won for the seventh time in eight games.
Marlon Byrd added two RBI in the victory.
Clay Buchholz (3-1) earned the win despite yielding six runs on seven hits in a 6 2/3-inning effort.
Athletics starter Tommy Milone (3-2) was pounded for eight runs (seven earned) on eight hits before being yanked after 4 2/3 frames.
Former Red Sox player Josh Reddick cracked a three-run homer and Coco Crisp added two RBI for Oakland, which dropped the first of a three-game set at Fenway Park.
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