Mike Moustakas had a three-run double for the Royals, who went 7-2 on their California road trip and scored at least seven runs in six of those victories.
Vargas (10-3) gave up three runs and eight hits in six innings. Facing a bases-loaded jam with nobody out in the sixth, Vargas was able to limit the damage to one run before departing.
Perez launched a drive to center field for his 14th homer of the season, leaving Cameron Maybin to climb the wall for show as part of a four-run outburst in the fourth.
Moustakas doubled in the third with the bases loaded, giving him 19 RBIs this month.