With the game tied 2-2 in the eighth, Young led off the inning with single against Wilton Lopez (1-4) and one out later went to second when Marlon Byrd flew out to deep center field.
After Ike Davis was intentionally walked, Juan Lagares (2-for-4, three RBI) hit a tapper to second baseman DJ LeMahieu, whose throw to first was late. Young, however, rounded third and headed home, catching the Rockies by surprise.
He slid in safely and the Mets held on to take the first contest of a three-game series.
Charlie Blackmon socked a solo homer for the Rockies.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Campus cop fatally shoots Texas student during traffic stop