Shane Bieber and two relievers combined on a four-hitter as the Indians blanked the Rays 2-0 in St. Pete.
Bieber struck out 11 while pitching three-hit ball into the seventh for his 10th win. Cody Allen closed it out for his 27th save.
Yan Gomes hit a solo homer in the fifth inning and Edwin Encarnacion went deep in the sixth for the Tribe.
The Indians and Rays play the rubber match of their three-game series in St. Pete this afternoon.
Cleveland is 82-and-63, 15-and-a-half games ahead of the Twins for first in the AL Central.
Carlos Carrasco toes the rubber for the Indians opposite Tampa Bay's Blake Snell.