The Diamondbacks won for the seventh time in nine games thanks to a combined one-hit effort by four relievers.
The game was tied at 3-3 in the fifth when Young delivered a one-out single off Chad Billingsley (0-4). Stephen Drew then doubled Young to third and, with Orlando Hudson batting, Billingsley uncorked a wild pitch that allowed Young to score.
After Hudson walked, Conor Jackson produced a fielder's-choice grounder to third on which Drew scored.
Arizona starter Edgar Gonzalez (1-1) got the win, giving up seven hits and three runs over 5 1/3. The only hit allowed by the Diamondbacks' relievers was a run-scoring single by Matt Kemp in the seventh that brought the Dodgers within 5-4.
Justin Upton gave Arizona an insurance run in the eighth with a sacrifice fly.
Brandon Lyon worked a perfect ninth for his sixth save.