Trailing 6-5 entering their final at-bat, the Rockies got one-out singles from pinch-hitter Wilin Rosario and Eric Young against Brewers closer Jim Henderson (0-2).
That brought up Colvin, who proceeded to smack a pitch down the right-field two chase home both with the game-winning tallies, enabling the Rockies to complete a three-game sweep.
The rally made a winner of Will Harris (1-0), who hurled two perfect innings in just his second major league appearance.
Young also cracked a solo homer while Chris Nelson went 2-for-4 with three RBI in the victory.
Nyjer Morgan drove in three runs with a pair of hits and Rickie Weeks went 3-for-5 with an RBI double for Milwaukee.