Blackburn (2-4) had not appeared since May 16 due to a strained leg muscle. Yuniesky Betancourt launched a two-run homer in the first off Blackburn that gave the Royals a 2-1 lead, but the Twins rallied for their fourth victory in five games.
Kansas City starter Felipe Paulino had to leave the game in the first inning after being hit in the leg with a hard hit ball off the bat of leadoff man Ben Revere.
Paulino recovered to throw out Revere at first and stayed in the game for three more batters before being removed.
The loss went to Luis Mendoza (2-3), who pitched five innings in relief of Paulino. Matt Capps worked the ninth for Minnesota and recorded his 14th save.