The Rockies won their third in a row after letting a two-run lead get away in the sixth.
Jason Giambi singled to open the ninth against John Axford (0-1) and Young came in as a pinch-runner. Young took second when Axford's pickoff attempt sailed wide for an error, and moved to third on a fly ball by Marco Scutaro.
That brought up Cuddyer, who singled to center on a 1-1 pitch.
Rafael Betancourt gave up a one-out double in the bottom of the 10th but got the next two batters for his fourth save.
The win went to Matt Belisle (1-0), who retired the only two men he faced in the ninth.
2014: The Year in Music [PHOTOS]