The Phoenix pulled clear of their fellow strugglers with a second half sucker-punch from Stein Huysegems, the 1-0 win confirming Heart as the A-League's worst side.
Speculation about Aloisi's future will reach new highs after Wellington took their chances in a largely poor quality match.
The Heart are now winless over 17 games dating back to last season.
The signs were there early on Friday night, Heart giving up possession at the first kick-off before the ball had left the centre circle.
While struggling to retain possession, both sides created chances early: Jeremy Brockie scuffed lazily wide from a long ball before Carlos Hernandez, Wellington's key attacking asset, struck the outside of the post in the first ten minutes.
Heart looked most dangerous down the right where Jason Hoffman's delivery and Michael Mifsud's pace combined to present David Williams an easy back post chance which he struck wide.
Wellington's quick ball movement was causing Heart problems but they could not turn their chances into goals.
Brockie went close at the near post after the break, before Aziz Behich danced his way into the box only to fire straight at Phoenix keeper Glenn Moss.
Harry Kewell was having his most anonymous game in a Heart shirt, and when he missed a simple trap after 51 minutes, a collective sigh went around the largely empty stadium.
With Heart in the ascendancy, another two chances were spoiled on the hour mark.
First a Behich centre found Moss from just a couple of metres out, while the resulting scramble was sent into orbit by Williams.
It was then Kewell's turn to miss, curling one from the edge of the box centimetres wide of the far post.
After 74 minutes Phoenix broke the deadlock with an old-fashioned tap-in.
Substitute Tyler Boyd broke clear of Behich and placed his cross at the feet of Huysegems who inexplicably found space so close to the Heart goal.
It could have been worse for the Heart, with Boyd denied by a last ditch Rob Wielaert tackle.