For a side who's season was basically on the line today, they were flat at the Cake Tin in front of 6453 people, who braved the wind and overcast conditions.
There was little to report from the first half, although the Phoenix should have taken the lead just before the split when striker Stein Huysegems was played through nicely by Manny Muscat.
The Belgian import only had Adelaide goalkeeper Eugene Galekovic to beat but he produced a weak shot which was palmed away by the custodian.
Huysegems has been the subject of speculation surrounding his future recently given he wants a two-year contract extension from the Phoenix but the club have only offered him a one-season deal.
The 31-year-old has scored 10 goals this season, the most of any Phoenix player, but he has also sprayed his share of notable chances, including today's effort before he was eventually subbed in the second spell.
The game needed to be ignited with a goal and it was Adelaide who found their way on to the score sheet first after Phoenix skipper Andrew Durante fouled Tarek Elrich in the box.
Referee Peter Green had no hesitation pointing to the spot to award Adelaide a penalty, which was calmly finished by Marcelo Carrusca with a neat chip just before the hour-mark.
As the home side went searching for goals, Phoenix coach Ernie Merrick went to his bench as Roy Krishna filtered in to the contest and he seemed an unlucky player to miss out on a start given his dangerous displays in recent weeks.
The Fijian international was his typical lively self when he came off the pine and he has clearly received a confidence boost since the club offered him a contract extension last week.
Phoenix midfielder Carlos Hernandez was also given a gallop off the bench after missing the past two weeks with a calf tear but was unable to impose himself on the contest.
Despite needing a victory, Wellington failed to produce any moments of magic in the final half an hour as the game ground to its uninspiring finish.
Adelaide United 1 (Marcelo Carrusca 58 pen) Wellington Phoenix 0 Halftime: 0-0