Carrasco (11-5) gave up two hits in eight innings and struck out 10 on 106 pitches (73 strikes).
Cleveland (61-52) scored five runs in the fifth inning.
Logan Morrison, Mallex Smith and Trevor Plouffe had the only two hits for the Rays (59-58). The Rays have been shut out four times during the first seven games of a nine-game homestand.
Rays starter Jake Faria was perfect through four innings before running into trouble in the fifth.
Edwin Encarnacion led off the inning with a solo home run over the 404-foot sign in center to give the Indians a 1-0 lead.
The next three Cleveland batters reached base and Jay Bruce scored on a sacrifice fly by Bradley Zimmer to double the advantage. Giovanny Urshela ripped a single to the right side that bounced off Evan Longoria‘s wrist and into right field to score Carlos Santana. Austin Jackson added an RBI on a fielder’s choice and Jose Ramirez had a run-scoring double to push the lead to 5-0.
Carrasco held the Rays without a base runner until he walked Steven Souza Jr. in the bottom of the fifth.
NOTES: Rays 3B Evan Longoria left the game in the fifth inning with a right thumb contusion. X-rays on the thumbs were negative. … Indians 2B Jason Kipnis will test out his sore hamstring on Saturday according to manager Terry Francona. If Kipnis cannot play, the team will consider the 10-day DL. … Rays OF Kevin Kiermaier took batting practice Friday and will play rehab games with Class A Port Charlotte as a designated hitter over the weekend. … Indians LHP Andrew Miller threw a bullpen session Friday and is expected to throw another Sunday. He is eligible to come off the 10-day disabled list Sunday.