Paul Ifill's late penalty was enough to take the New Zealand club through to the second week of the finals after a five-goal thriller against the Sky Blues
The two sides were goalless after a dour first half which produced more bookings than genuine chances.
While Brown's goal in the 47th minute broke the deadlock, the match came to a thrilling conclusion in a seven-minute burst that produced four goals, including a penalty from Paul Ifill that ultimately decided the contest.
A Ben Sigmund header doubled the Phoenix's lead and looked to have booked their place in next weekend's minor semi-final until Joel Chianese completed a quickfire double to get the visitors right back on level terms.
But with four minutes of regular time to go, Ifill was brought down in the box by Michael Beauchamp and he made no mistake from the spot.
Nick Carle almost got Sydney off to the dream start with just three minutes gone but his shot was deflected off a Phoenix defender and the corner was then wasted.
The next real opportunity for the visitors came 15 minutes later when a great ball from Karol Kisel put Chianese clear. His cross looked to have left Cazarine a simple finish but Sigmund got his foot to it and blazed it over his own goal.
Some outstanding goalkeeping from Ivan Necevski then denied Wellington the opener after Ifill had won a corner.
Leo Bertos curled the ball in but a great reflex save from the Sydney keeper kept out Andrew Durante's header.
The flurry of yellow cards followed in the next 20 minutes as both teams became frustrated with their lack of progress. Scott Jamieson, Tim Brown, Dani Sanchez and Bruno Cazarine were all booked and teams remained goalless at the break.
The match was eventually broken open in the 47th minute when Brown, who will retire from football at the end of the season, delivered the goal the partisan 10,019 crowd had been waiting for.
Shannon Cole got a head to Bertos's free-kick but it went only as far as Sigmund on the left-hand edge of the box. The big defender headed it down and Brown poked it home.
Sydney's woes continued as Pascal Bosschaart was then forced off with injury in the 49th minute to be replaced by Sebastian Ryall.
Ifill had scored in all three previous wins against Sydney this season but could not get the better of Necevski in the two minutes before the hour. A great ball from Chris Greenacre put the Barbados international through on goal but under pressure from Beauchamp he only succeeded in chipping straight at the Sydney keeper.
The veteran striker had said earlier in the week that cutting out the delivery to Cazarine would go a long way to helping the Phoenix win the game. The Brazilian was given very few chances and was eventually substituted for Mark Bridge in the 60th minute.
But the drama really began from the 79th minute when an unmarked Sigmund headed his side in front.
From the restart Sydney scored as Nick Carle's deft touch was flicked on by Karol Kisel and Chianese provided the finish.
The midfielder was on target again a minute later when Paston failed to hold to Bridge's shot and Chianese pounced to set up a thrilling finale.
It was eventually decided by Ifill's penalty as he kept up his record of scoring in every one of the Phoenix's victories over Sydney this season.