The A's outscored the Royals 26-8 in the series.
Bobby Crosby had three hits and an RBI for Oakland, which scored five runs in the fourth inning after trailing early.
Dana Eveland (2-1) was the winning pitcher, allowing three hits and the lone Royals run in 5 2/3 innings.
Kansas City has lost four games in a row and five of six.
Luke Hochevar (0-1), the No. 1 overall pick in the 2006 draft, took the loss, giving up six runs on nine hits in 4 2/3 innings.