Carrasco was one strike away from the landmark before his historic bid was foiled when Joey Butler singled on a two-strike count.
The 28-year-old Venezuelan right-hander settled for a one-hit triumph after tossing 8 2/3 hitless innings, the one hit coming on a lofted shot over Cleveland second baseman Jason Kipnis.
Carrasco exited after a career-high 124 pitches to a standing ovation in the opposing ballpark. He struck out 13 batters and walked only two.
The South American hurler came within one pitch of being the first Indian to throw a no-hitter since Len Barker tossed a perfect game in 1981. He would have been the first Cleveland pitcher since 1948 to throw a no-hitter on the road.
It was the third game in a row in which a Cleveland pitcher started with at least five no-hit innings against the Rays.??
Carrasco, who improved to 10-6 this season, carried an 8-0 lead into the ninth innings as the drama about the no-hitter built with the mystery of who would win all-but over.
Carrasco, who hurled 6 1/3 perfect innings before walking Butler, issued his second walk of the game to Asdrubal Cabrera to open the bottom of the ninth inning and then walked pinch-hitter Brandon Guyer to put two Rays runners on base.
Grady Sizemore entered as a pinch hitter and grounded into a fielder’s choice, leaving runners at first and third bases with one out.
Carrasco made Kevin Kiermaier his 13th and last strikeout victim for the second out, bringing Butler to the plate.
With two strikes against him, Butler rapped a high lob just over the glove on the outstretched arm of a leaping Kipnis and sent the ball rolling into center field for a run-scoring single to break up the no-hit and shutout bids.
Carrasco smiled and point to Kipnis in respect for the fielder’s effort made to try to complete the no-hit effort.