Tony Popovic's side looked set to close the gap on Brisbane Roar at the top of the table to just one point when Mark Bridge gave them the lead just after the hour mark at the Parramatta Stadium.
However, Tyler Boyd equalised for the visitors five minutes later, before a late double from Stein Huysegems gave in-form Wellington their third win in a row.
Ernie Merrick's men's victory is made all the more impressive when taking into account their injury list, with Paul Ifill (Achilles) and Carlos Hernandez (wrist) missing out altogether and Louis Fenton and Jason Hicks picking up problems during Wednesday's match.
The result marks the first time in 27 A-League games that Wellington have scored over two goals in a match, and lifts them up to eighth in the table.
Western Sydney, meanwhile, remain second, but are four points adrift of pacesetters Brisbane having played a game more than Mike Mulvey's team.
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