The frantic trip to Auckland was worthwhile, with his ninth goal in 10 games and the fourth consecutive match he has found the net.
The victory keeps the Phoenix handily placed for the playoffs, four points clear of sixth-placed Sydney and one of three teams clustered on 28 points.
It wasn’t a vintage display from the Phoenix, who struggled for fluency and spent much of the second half camped in their own half.
It made for a nervy watch for the 10,420 crowd but at this stage of the season results are all that matter, while it also meant their unbeaten streak at Eden Park – dating back to 2011 - continues.
Perhaps understandable with what was at stake, it was a cautious, cagey start from both sides.
Sydney striker Robert Mak had the best early chance, unlucky to find the woodwork after his angled strike had beaten Oli Sail.
But Zawada’s goal was a beauty.
After a period of sustained possession, a clever ball from Yan Sasse created an overlap, before a deep Lucas Mauragis cross found Zawada at the far post.
It was another example of the Polish striker’s aerial prowess, as he hung in the air brilliantly, before powering his header back across the keeper, for his 12th goal of a memorable personal campaign.
That kicked the Phoenix into gear, as their passing became crisper and runs more assertive.
David Ball went close with a near post flick from a Sasse corner, before the Brazilian – who was the Phoenix standout of the first half – forced a sprawling save from Sydney keeper Andrew Redmayne, after a 20-metre drive.
Apart from Mak’s effort, Sydney had few chances in the first period.
But the Phoenix rode their luck, as they failed to pressure the cross and close down the man in possession, while the visitors enjoyed plenty of time in the final third but couldn’t find the decisive touch or pass.
Sydney should have equalised early in the second half, but Rhyan Grant’s delicious ball went untouched across the six-yard box.
Zawada then went close – just failing to connect with an inviting cross from Ball.
The Phoenix continued to be sit deep, looking to break on the counter, but they were guilty of being too passive at times, opting to recycle when a direct approach was justified.
Sail was the far busier keeper in the last 30 minutes, but the Phoenix held firm with their rear guard action, as Sydney eventually ran out of ideas.
Wellington Phoenix 1 (Oskar Zawada 21)
Sydney FC 0
