Jumping on an 0-2 delivery from Marco Estrada, Lindor broke the pitching deadlock in the bottom of the sixth with a shot 412 feet to right-centre field after Jason Kipnis walked before a sellout crowd of 37,727 at Progressive Field.
It was the Jays' first loss in five games this post-season. Cleveland extended its playoff win streak to four.
Estrada (1-1) had cruised through the early innings, facing minimal resistance, and recovered after the home run in a 101-pitch, six-hit outing. He deserved better in posting the first complete game of his career, and the first by a Jay this season.
Jays had chances
Cleveland ace Kluber (2-0), meanwhile, had to dig himself out of one early one hole after another before finding his groove. Andrew Miller came in with one out in the seventh and struck out five of the six hitters he faced.
Closer Cody Allen pitched a 1-2-3 ninth, earning his third save.