Parker (4-3) yielded only one run while working around four walks and striking out nine. It was the rookie right-hander's third consecutive start in which he's allowed one or fewer runs.
Parker tossed 65 of his 104 pitches for strikes and lowered his ERA to 2.57 as the A's claimed the rubber match of their three-game road series and improved to 11-4 since June 12.
Grant Balfour hurled a scoreless eighth and Ryan Cook picked up his sixth save.
Coco Crisp socked a solo homer in the first inning and Yoenis Cespedes broke a 1-1 tie with a seventh-inning blast off Hisashi Iwakuma (1-1).
Seattle starter Kevin Millwood allowed one run over 2 2/3 innings before leaving the game with a groin injury.
John Jaso homered for the Mariners.