Ji-Man Choi hit a walk-off, two-run homer in the ninth inning to lift the Rays past the Indians 6-5 in St. Pete.
Brandon Guyer hit a two-run double in the sixth to tie the game for Cleveland, which has now lost three-of-four.
The Indians took a 5-4 lead on a Yonder Alonso RBI groundout in the seventh.
Brad Hand blew the save and was charged with the loss.
The Indians play the second of three games against the Rays at The Trop tonight.
Cleveland is 81-and-63, 15-and-a-half games ahead of the Twins for first in the AL Central.
Shane Bieber toes the rubber for the Indians opposite Tampa Bay's Tyler Glasnow.