Greinke (3-0) allowed one run, striking out four and walking just one.
Jarrod Washburn (1-2) yielded three runs on six hits in six innings, with six strikeouts and no walks for the Mariners.
Ichiro Suzuki drove in the only run for Seattle.
After Butler led off the second with a homer, Jose Guillen doubled and then scored on Olivo's homer.
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