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.