The new season began after thunderstorms caused a 14-minute delay at the start.
Once the weather cleared, Miley threw the first pitch. It was a called strike to Yasiel Puig, who struck out on three pitches.
Aaron Hill got the first hit of the regular season, an infield single for Arizona off NL Cy Young winner Clayton Kershaw in the first inning.
Adrian Gonzalez drew a leadoff walk in the Dodgers second, moved up on a double by Van Slyke and scored the first run on a groundout by Andre Ethier.
Arizona third baseman Martin Prado made the first error, throwing away a grounder by Hanley Ramirez in the fifth.
This is the first regular-season game that MLB has played in Australia. The Dodgers and Diamondbacks are set to wrap up their two-game series on Sunday.
The long trip to the opener took even longer for some Arizona players.
One of the team buses had a flat tire, and the Diamondbacks said ''a handful'' of players and some staff decided to walk the last half-mile to the stadium instead of waiting for a replacement bus to arrive.