Anderson (4-0) won for the fourth time in four starts since returning from elbow surgery, during which he has yielded just two earned runs in 26 innings for a 0.69 ERA.
The left-hander scattered six hits, didn't allow a walk and struck out four for American League wild card-leading Oakland, which clinched its three-game series.
George Kottaras clouted a two-run homer and Coco Crisp went 2-for-4 with an RBI double for the A's.
Seattle's Hisashi Iwakuma (6-4) was knocked around for five runs (four earned) on six hits over 3 2/3 innings.
Trayvon Robinson knocked in the only runs for the Mariners.