Wil Myers led off the ninth against Greg Holland (0-1) with an infield single and later moved to second on a wild pitch with two outs. Loney then laced a single to right field to plate Myers for the go-ahead run.
Mike Moustakas reached in the home half with a lead off single, but Grant Balfour retired the next three hitters in order to pick up his second save.
Rays starter Chris Archer scattered six hits and struck out four over seven scoreless frames. Joel Peralta (1-1) recorded the final out of the eighth to earn the win.
Kansas City starter Yordano Ventura allowed just two hits and struck out six without walking a batter over six scoreless innings.
The Royals were 2-for-8 with runners in scoring position, but left the bases loaded three times.