But the Phoenix had several decent chances in the final 30 minutes, with two good opportunities falling to Roy Krishna.
The result continued an unwelcome pattern - Wellington have won only one of their 10 season-opening games - but there were some encouraging signs tonight. Gui Finkler showed some handy touches as well as efficient dead-ball delivery, while new defenders Marco Rossi and Jacob Tratt had plenty of endeavour. But Roly Bonevacia had a quiet game by his high standards and Alex Rodriguez will need to show more this season to justify his import status.
Tonight was always going to be an uphill battle. Facing the best attacking side in the league without three of the side's best players and a completely new back four could have been a recipe for disaster. Andrew Durante, Michael McGlinchey, Kosta Barbarouses, Matt Ridenton and Louis Fenton were all absent, part of the All Whites squad to face Mexico tomorrow. It will be a recurring issue throughout this season, with the A-League's ongoing refusal to make allowances for Fifa international windows.
The depth disparity was reflected in the make-up of the respective benches. City had three reserves with more than 100 A-League appearances each, while the entire Phoenix bench had nine A-League matches between them.
Melbourne could have taken the lead as early as the second minute, with only a desperate clearance from Vince Lia preventing a gilt-edged opportunity. Glen Moss, who continues to be unwanted at international level, distinguished himself with two impressive early saves, the second drawing a surprised smile from 2015 A-League golden boot Bruno Fornaroli.
The visitors took the lead in the 27th minute, with Anthony Carceres latching onto a precise diagonal ball from the impressive Bruce Kamau and slipping past Moss before lashing into an empty net.
City probably should have been further ahead at halftime - with 11 shots on goal (five on target) - but the rookie Phoenix backline rode their luck and showed admirable persistence.
Krishna forced a good save at the near post at the other end and had another chance fall his way, but replacement City goalkeeper Dean Bouzanis distinguished himself in just his second appearance in two seasons.