Diamond (1-0), making his first start of the year and the eighth of his major-league career, baffled the Angels on four hits, issuing only one walk and striking out six.
The 25-year-old left-hander tossed 62 of his 103 pitches for strikes as the Twins won for only the second time in May.
Angels starter Dan Haren (1-3) was tagged for all five runs on eight hits in a 3 2/3-inning effort.
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