Morneau's homer came during a six-run outburst in the fourth inning.
Denard Span and Delmon Young each drove in a run for the Twins, who have won four of their last five.
Blackburn (7-4) allowed two runs and seven hits, striking out six batters. The complete game was his third this season.
Brandon Inge hit a two-run homer for the Tigers.
Loser Rick Porcello (8-6) gave up all the Twins' runs and seven hits in four innings.
Copyright 2009 by United Press International.