Morneau, who has only played 150 games the past two seasons because of several injuries, had five RBIs as the designated hitter.
Rookie of the Year winner Jeremy Hellickson gave up 10 runs and 11 hits, including three home runs.
Infielder Luke Hughes, who could be in the mix for the first base job if Morneau spends most of his time at DH, went 5 for 5 with a home run and two doubles for the Twins. Shortstop Jamey Carroll added three hits and a double.
J.R. Towles and Chris Parmelee also homered for the Twins.