Making his first home start as a Royal, Vargas made it a good one, holding the Rays to four hits in eight-plus innings to pick up his first win of the season.
"It was a good night, we were able to execute early, make pitches down in the zone," Vargas said. "If we do that, we can be effective."
Of the 110 pitches Vargas threw, 74 were strikes.
"He was just locating really well, mixing up his pitches really well and keeping the ball down," said Wil Myers, who went 0-for-4. "I didn't see too many mistakes that he made over the plate."
Rays manager Joe Maddon also complimented Vargas, who last defeated the Rays 2-0 while pitching for the Angels on Aug. 29 at Tropicana Field, when he allowed just two hits in seven scoreless innings.
"He's a fly-ball pitcher," Maddon said. "He knows what he's doing. He gets a lot of fly balls in the middle of the field. ... He's a very good pitcher and I've always admired and respected him.
"Not unlike what [Mark] Buehrle did to us several days ago [when the Blue Jays defeated the Rays 3-0 on Wednesday]. A similar outing. Vargas probably has more of a fastball than Buehrle, but they pitch in a similar manner."
Ben Zobrist finally chased Vargas when he led off the ninth with his first home run of the season.
"It was right over the heart of the plate," Vargas said. "He put a good swing on it and that's all she wrote."
Royals manager Ned Yost lifted the left-hander after Zobrist's blast and brought in Greg Holland, who surrendered an RBI single to pinch-hitter Matt Joyce, but managed to get the final three outs to preserve the victory and earn his third save of the season.
"You never know [if you're going to get the shutout] until it's all said and done, but if you don't try, you can't get one," Vargas said. "The defense made some great plays tonight, some huge plays. It could've been a lot different game."
Vargas got offensive support from the beginning. Nori Aoki tripled to left against Matt Moore leading off the first then scored one out later on Eric Hosmer's single to left, giving the Royals a 1-0 lead.
Moore then escaped further damage in the first and he managed to dodge potential disasters in the second and third innings when he retired the side in order, the final two on strikeouts.
Moore had to leave the game when he felt left-elbow soreness after he retired the first batter in the fifth.
"He was doing good," Maddon said. "He and [Ryan Hanigan] were getting into a nice little rhythm right there. I did see it turning in our favor at that point. But we came up short. But I thought there were some positives too."
Cesar Ramos took over for Moore and retired the final two batters in that inning.
Heath Bell relieved Ramos with one on and one out in the sixth and the Royals loaded the bases after a single to right by Savalador Perez and an infield single by Lorenzo Cain. Alcides Escobar then emptied the bases with a two-out double to push the Royals' lead to 4-0.
Escobar is a career .356 hitter against the Rays. He has eight doubles in 20 games against the Rays.
"Escobar hits a ball in the corner, he's just on that all-negative-opponent team with the Rays and Devil Rays," Maddon said. "This guy always hurts us."
Bell's stint was marred by what happened in the sixth when he hit leadoff batter Omar Infante on the jaw.
"I felt pretty good tonight," said Bell, who pitched 2 2/3 innings. "Made two mistakes. One hitting Infante and a pitch up to [Escobar]. "I was trying to throw a sinker and just let it run and it ran too much and just didn't finish it. It went up and in. ... I feel really bad. I know he feels bad, but I feel worse."
The Rays have now taken seven consecutive losses at Kauffman Stadium and have not won there since July 24, 2011.