The host required only a point to make certain of a top-six finish and it was ahead inside 11 minutes when Ziggy Gordon turned Ryan Strain's shot into his own net.
However, Wanderers had lost only one of their last eight league meetings away at United and were back on level terms thanks to a Bruce Kamau shot that deflected in off Strain.
Carl Robinson's side had been eliminated from the top-six picture before kick-off yet they found themselves ahead against United through Graham Dorrans' low drive with half an hour played.
A red card for Tass Mourdoukoutas six minutes later following a reckless challenge on Louis D'Arrigo gave United hope but the visitors held firm until the 56th minute.
Goodwin peeled away at the back post and thumped a low shot past Daniel Margush for his third goal in five games.
That proved to be it as Carl Veart's men held on to pick up a draw which keeps them on course for A-League glory and ended Wellington Phoenix's Finals hopes in the process.