The lefty gave up just one run over eight innings while Alcides Escobar knocked a three-run double to life the Royals to a 4-2 win in their series opener with the Rays.
Needing a long outing with a depleted bullpen, Vargas (1-0) went to the ninth inning before giving up a solo home run to Ben Zobrist on his final pitch. Tim Collins (elbow flexor) and Francisley Bueno (finger sprain) were sent to the 15-day disabled list Monday afternoon. Donnie Joseph and Michael Mariot were called up.
Both Vargas' strikeouts came in the game's first two at-bats, including Wil Myers, who is playing his first full series in Kansas City since being dealt to the Rays (4-4) in exchange for James Shields and Wade Davis. He went 0-for-4.
Eric Hosmer drove in Nori Aoki to establish a 1-0 lead in the first frame. Escobar's sixth-inning drive came within feet of being the team's first home run of the season.
Greg Holland allowed Matt Joyce to cut the lead to two with an RBI single, but closed the door with a strikeout for his third save.