Vogt broke a 2-all tie with a bloop single to left field in the eighth inning. The A's catcher had two passed balls that were big factors in Oakland's 6-4 loss in the series opener Friday night.
Fernando Rodriguez (4-1) pitched two innings for the victory. The A's won at Arizona for the first time since June 17, 2008.
Drew Pomeranz struck out the side in the ninth for his third save as the Diamondbacks fell to 1-5 on their homestand.
Andrew Chafin (5-1) took the loss.