Vargas (8-7) logged his sixth career complete game and notched his first victory since June 4, a span of five starts.
The left-hander yielded just one run, issuing a single walk and striking out six while placing 66 of his 107 pitches for strikes as Seattle evened its three-game road series.
Kyle Seager supplied a bases-clearing double in the fifth inning, while Casper Wells socked a solo homer and Brendan Ryan added two RBI for the Mariners.
Athletics starter Jarrod Parker (5-4) gave up six runs (five earned) on six hits in a 4 2/3-inning effort.
Josh Reddick went 2-for-4 with a bases-empty clout for Oakland.
Celebrity Couples of 2014 [PHOTOS]