It was the third career start for Straily (1-0), who helped the Athletics snap a three-game losing streak. He threw 99 pitches, gave up three hits and struck out two before the game was turned over to the Oakland bullpen.
Sean Doolittle relieved Straily with one on and one out in the seventh and loaded the bases before getting out of trouble.
Relievers Jerry Blevins and Ryan Cook both saw duty in the eighth and Grant Balfour came on in the ninth to collect his ninth save.
The game was scoreless into the sixth before Coco Crisp put Oakland in front with a solo homer. Yoenis Cespedes hit a homer in the seventh and Jemile Weeks singled in a run in the eighth.
The loss went to Luke Hochevar (7-11), who allowed all three runs on four hits in seven innings.