Mastroianni collected a two-out single in the 12th against Scott Maine (1-1) -- the Tribe's club-record 10th pitcher -- and stole second to get into scoring position.
Alexi Casilla then hit a routine grounder to second baseman Jason Kipnes, but first baseman Matt LaPorta didn't cover the bag in time, allowing Mastroianni to come around and slide home for a 5-4 Twins lead.
Pedro Florimon then gave Minnesota a much-needed insurance run with an RBI single.
Lonnie Chisenhall socked a solo homer for Cleveland.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
N.J. man wakes up from 10-hour sleep with knife in back