Brendan Harris had a two-run shot for the Twins, who took three-out-of-four in the season-opening series.
Minnesota starter Kevin Slowey (1-0) pitched 5 1/3 innings, giving up one run on seven hits with two walks and three strikeouts.
Maicer Izturis drove in the Angels' only run.
Joel Pineiro (0-1) allowed three runs on five hits in six-plus innings for the Angels.
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