With the score tied 2-2 in the eighth, McCutchen drew a one-out walk from Scott Rice (0-1).
Justin Wilson (3-0) earned the decision despite allowing a score-tying run in the seventh and Jason Grilli racked up his National League-best 15th save as Pittsburgh notched its fourth win in six games overall.
Clint Barmes went 2-for-4 with a homer in the victory.
Lucas Duda went deep for the Mets, who fell to season-worst six games under .500 (14-20).
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