The Mets were behind 2-1 in the eighth when they capitalized on a pair of Brewers errors to grab the lead.
Juan Lagares reached on an error by Brewers shortstop Jeff Bianchi, then scored the tying run all the way from first when catcher Jonathan Lucroy threw away Juan Centano's sacrifice bunt.
Pinch-runner Matt den Decker moved up an out, and after Josh Satin flied to shallow right, Young's slow grounder off Brandon Kintzler (3-3) was enough to send him home with the decisive tally.
Vic Black (3-0) earned the decision and Frank Francisco recorded his first save as the Mets (74-88) avoided a four-game sweep to end the season.
The Brewers (74-88) finished the year with four wins in five games.