Steven Souza Jr.'s three-run homer paced the four-run first. Brad Miller hit a solo shot and Kevin Kiermaier added a three-run homer to account for most of the Rays' scoring.
Jake Odorizzi started for the Rays and continued his recent run of excellence with his third consecutive scoreless start, allowing just two hits in six innings to move to 6-5 on the season.
Edinson Volquez started for the Royals and struggled from the rough first inning until he made his exit in the sixth inning with eight runs (seven earned) and 11 hits showing on his line, falling to 8-10.