The Polish striker needed 25 minutes to rediscover his scoring touch after missing the 5-1 thrashing by Adelaide for the birth of his child. Zawada pounced on a defensive mistake from Damien Da Silva to lob goalkeeper Paul Izzo, finding the net in his fifth straight game while taking his season total to 13.
But after Izzo produced a couple of crucial saves to deny Yan Sasse and Steven Ugarkovic, Melbourne made their opponents pay for lapses in set-piece concentration.
First, the Phoenix failed to track Bruno Fornaroli’s run and allowed him to nod in an equaliser on the hour mark. Then, Da Silva atoned for his error by heading home another corner in the 76th minute, leaving captain Alex Rufer frustrated.
“We were poor from set pieces and they punished us,” he told Sky Sport. “We switched off. It’s not an individual; it’s collectively.
“We need to be better from those moments and we let ourselves down massively.”
Rufer remained hopeful his side could earn the top-four finish they required to host a playoff game, despite having to head across the Tasman for three of their final four matches.
“It’s a big blow, but we’ve got four games left,” he said. “We know where we are. Yes, it’s disappointing, but we go again. We believe in ourselves, we’re a good team, and it’s down to us now.”
The Phoenix women, meanwhile, have earned the wooden spoon for the second straight season, with a 99th-minute equaliser against Melbourne Victory not enough to climb out of 11th place.
Wellington required a win over the defending champions to have any hope of avoiding that unwanted prize, but those chances were grim when the visitors scored two superb goals in the first 26 minutes.
Alana Murphy put Melbourne in front by putting a free kick in the top corner from the edge of the box, before Melina Ayres turned Marisa van der Meer and fired high into the net from a tight angle.
The Phoenix pulled back a goal with 15 minutes to play when Victory custodian Casey Dumont couldn’t clean up trouble outside the area, leaving her goal unguarded for Ava Pritchard to make it 2-1.
Grace Wisnewski then managed to bundle home a leveller with virtually the last kick of the game, ending the campaign on a positive note.
Having finished their inaugural season with two wins, seven points and a goal difference of minus-23, the Phoenix at least improved on each count, collecting three wins, 13 points and finishing on minus-10.
But with the final position the same, Wellington will have to content themselves by playing potential spoiler for Melbourne, leaving the Victory relying on other results to remain in the top four and sneak into the semifinals.
Melbourne Victory men 2 (Bruno Fornaroli 58, Damien Da Silva 76)
Wellington Phoenix men 1 (Oskar Zawada 25)
Wellington Phoenix women 2 (Ava Pritchard 75, Grace Wisnewski 90+9)
Melbourne Victory women 2 (Alana Murphy 4, Melina Ayres 26)