Vargas threw 98 pitches and effectively spotted his fastball, which set up his changeup.
"He pitches you in, he pushes you off, you see guys moving their feet a lot," A's manager Bob Melvin said. "Then, he throws you changeups away and doesn't throw anything in the middle of the plate. He pitched well."
Vargas gave up just four hits and struck out eight. His second win of the season also lowered his ERA to 0.66.
"Awesome. He was unbelievably good," Royals manager Ned Yost said. "I don't think he missed too many spots today."
Vargas said he used a similar plan to the one he used in Houston on Friday.
"I think it all fed off being able to get ahead with the fastball, opening things up for the other pitches early in the count, late in the count, then later in the game," Vargas said. "Being able to command the fastball early definitely opened some doors in those middle innings and later innings."
Vargas rarely had to navigate through any trouble. But the A's had something brewing in the fourth inning when slugger Khris Davis came up with one on and one out.
Vargas fell behind 3-0, but he then threw a changeup and Davis grounded into a double play. Davis had pounced on a 3-0 fastball from Ian Kennedy on Monday and hit a two-run homer.