Harvey (3-0) reduced his ERA 0.82 with the 107-pitch performance, in which he yielded one run, walked two and struck out six in his third dominating victory in three starts.
Bobby Parnell recorded his first save of the season despite allowing a run in the ninth for the Mets, who clinched their three-game interleague series and improved to 7-4 overall.
Minnesota's Scott Diamond (0-1) took the loss in his season debut, surrendering four runs on eight hits over 4 1/3 frames.
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