The 26-year-old has bagged 10 goals this season to lead the Golden Boot standings by three.
It comes after a nomadic few seasons of professional football when many questioned whether he would ever live up to vast amount of potential he showed as a teenager.
Wellington tried to take advantage of Roy Krishna's pace in the early stages against Sydney by trying to release the Fijian international on goal but Sydney goalkeeper Vedran Janjetovic played a high line and was equal to Krishna's advances.
Janjetovic had to play virtually as a faux sweeper, which looked a risky strategy given the speed among the Phoenix's front three.
As well as Burns' form, Krishna had scored in his last four games.
The home side enjoyed the run of the race during the opening 45 minutes but, despite having a raft of possession, were unable to score.
Wellington's midfield struggled to gain parity, which didn't allow them to stamp their mark on the contest as Roly Bonevacia and Alex Rodriguez didn't provide enough of an influence but they managed to work their way in to the game during the second spell.
The enjoyed greater possession, without really threatening, until Burns injected himself on the game.
Conditions were quirky with a stiff breeze, glaring sunlight and a bumpy Allianz Stadium surface in Sydney all adding to the challenge for the players.
The Phoenix were without the suspended Manny Muscat, which gave Tom Doyle a reprieve at left-back. The 22-year-old Doyle, who was impressive during the pre-season but has provided up-and-down service during the campaign proper, was solid on his return to the starting side.
The Phoenix will return to the comforts of home when they host the struggling Western Sydney Wanderers in Wellington next Sunday.
The Wanderers, despite their success in the Asian Champions League, have struggled on the domestic front this season and are anchored to the foot of the A-League ladder.
Wellington Phoenix: 2 (Nathan Burns 73, 81)
Sydney FC: 0 (Halftime: 0-0)