Straily (2-0) allowed three runs on seven hits over 6 2/3 innings and struck out eight Los Angeles batters in the process to keep the A's three games behind front-running Texas.
Brandon Moss hit a solo home run and Yoenis Cespedes added a solo shot for the A's. Tuesday's win gave Oakland its 11th consecutive road win, a feat they last accomplished in 1981.
Jerome Williams (6-8) took the loss after allowing four runs on five hits over just 3 1/3 innings.
Los Angeles led 3-1 after three innings but Oakland hung up three runs in the fourth to take the lead.