If they can play with the same sort of spirit and desperation in their final two games, they will be a chance. They worked tirelessly throughout as Melbourne dominated and only a combination of some wasteful finishing, good goalkeeping from Mark Paston (and Tony Lochhead) and some scrambling defence kept the Heart to a solitary goal.
Lochhead turned one shot around the post with his hands but was given the benefit of the doubt by the referee given it was blasted at him from relatively close range.
But Wellington had a good penalty shout of their own in the first spell when Ifill was bundled over in the box by Fred but the referee waved play off. Perhaps the whistle blower was evening things up but it was unsurprising a melee occurred less than a minute later as tempers boiled over.
It was the flashpoint in a sometimes feisty match saw players from both sides square off following a dangerous tackle from Andrew Durante on Jonatan Germano. There was pushing, shoving and a fair bit of gesticulating before Durante and central defensive partner Ben Sigmund saw yellow.
It was a reflection of what was at stake. The table is squeezing up and so is the pressure.
Melbourne deserved their halftime lead. They broke with pace and skill as they used the ball well but the Phoenix scrambled well. The goal they conceded was a soft one in the context of the match - Eli Babalj scored a far-post header from a free kick in the 32nd minute as he squeezed in between two defenders.
Wellington grew into the match in the second spell but made only rare forays into the box. For the most part they were toothless in attack or gave possession away too cheaply and expended most of their energy chasing Melbourne players in what was already a game played at a frantic pace.
It didn't help they lost Leo Bertos before the match, after the tricky winger who had rediscovered form over the last month cut his knee in training, and Lochhead still seemed to be suffering from the effects of the illness that kept him out last week.
The fans will have gone home happy from an entertaining match but players from both sides wanted more. A point is better than none, however.
Melbourne 1 (Eli Babalj 32) Wellington Phoenix 1 (Paul Ifill 80). HT: 1-0.