Kansas City overcame a two-run deficit with a run in both the eighth and ninth innings, but the Mets finally broke through against Luis Mendoza (2-6).
Omar Quintanilla drew a one-out walk in the 11th and, with two away, Young launched a 3-1 pitch over the wall in right.
Those were the first runs the Mets had scored since the first inning, when David Wright hit a two-run homer.
Young's home run, his second, gave the win to Carlos Torres (2-2). He worked the 10th and 11th innings, giving up two hits with a strikeout. New York had lost its previous two games.