Oakland ended a three-game losing streak and moved within 4 1/2 games of Texas for the lead in the American League West.
Kottaras broke a 1-1 tie with his homer, which came off Felix Hernandez (13-7).
Hernandez lost his second start in a row after having won nine straight decisions. He gave up five runs on 11 hits in 4 2/3 innings.
Oakland added two runs in the fifth on an RBI double from Josh Donaldson, who then scored on a single by Stephen Drew.
A.J. Griffin (5-0) worked 5 1/3 to get the win, surrendering a lone run on six hits while striking out seven.