A two-run single by Chris Parmelee in the seventh inning had rallied Minnesota to a 7-6 lead, but the Indians, who had gone up a 4-0 lead in the third and 6-5 in the fifth, pushed across a tying run in eighth on Jason Donald's one-out RBI triple.
Then in the ninth, Vinnie Pestano (3-2) served up a pitch Morneau hooked just inside the right-field foul pole for the win.
Brian Duensing (4-10) claimed the decision after recording the final out of the eighth with runners on the corners and following that up with a scoreless ninth.
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