Young smacked a two-run homer in the first inning to put Arizona ahead for good and added a run-scoring single two innings later.
Aaron Hill also drove in a pair of runs for Arizona, which avoided a three-game sweep at the hands of the Rockies.
Cahill (1-0) earned his first victory as a Diamondback after being acquired from Oakland in December. The right-hander held Colorado to one run on four hits over 7 1/3 innings, walking two and fanning six.
Rockies starter Drew Pomeranz lasted only 4 1/3 frames. He was lit up for five runs on nine hits.
Tyler Colvin and Troy Tulowitzki drove in runs for Colorado.