Miles connected on a trio of 3-pointers and went 8-of-13 from the field as the Cavaliers built a 91-75 lead with 5 minutes left in the game.
But the Wolves then reeled off a 17-2 run, sparked by six points from Corey Brewer, narrowing the gap to one point with 11 seconds remaining and possession of the ball.
Minnesota's Kevin Love, however, missed a 3-point try as time expired, and Cleveland notched the win, improving to 2-0 at home.
Kyrie Irving supplied 15 points, eight rebounds and six assists while Tristan Thompson helped out with 12 points and 11 rebounds for the Cavs.
Kevin Martin put in 23 points, including five 3-pointers, and Love finished with a double-double of 17 points and 13 rebounds for the Timberwolves, who suffered their first loss after starting the season 3-0.
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