Tommy Pham, Yandy Diaz and Ji-Man Choi each drove in a pair of runs as the Rays beat the Royals 8-5.
Yonny Chirinos improved to 4-0 by earning the win in relief of effective opener Ryne Stanek.
Brad Keller took the loss for Kansas City in his first game since serving a five-game suspension for his role in a fracas with the White Sox.
