Guthrie (2-3) allowed only one runner to get as far as second base, scattered three hits and issued a pair of walks.
Tim Collins and Greg Holland completed the gem with one scoreless frame each as the Royals hung a second straight shutout on the Athletics and clinched their three-game series.
A's starter Jarrod Parker (7-7) didn't make it out of the big frame, lasting 4 2/3 innings. The right-hander surrendered five runs (four earned) on five hits in dropping this third straight start.
Oakland fell 1 1/2 games out of an American League wild-card playoff spot.