The two homers were part of a wild game that included five ejections.
Morneau's homer staked the Twins to a 2-0 lead in the second inning. After Jody Gerut's RBI double halved the deficit in the third, Koskie responded in the bottom half as his homer gave Minnesota a 4-1 lead.
Both benches emptied, leading to the ejection of Hunter, Davis, both managers and Cleveland's C.C. Sabathia, the Indians' starter Thursday.
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