The Guardians split their four-game series with the Rays following a 2-0 win from Progressive Field.
Ben Lively gave up four hits and one walk over five innings to earn the win.
Emmanuel Clase notched his 45th save of the season while Brayan Rocchio drove in a run.
Cleveland remains first in the AL Central at 86-and-64.
The Guardians host the Twins tonight.