Substitute Terry Antonis fired the winner for the Sky Blues after the Wanderers had fought back from three goals down in a duel of multipe twists and turns.
The visitor had to play the final 10 minutes with ten men in front of an enthralled crowd of 19,484 after the dismissal of Mickael Tavares.
The win took Sydney above Wellington into fourth place while the Wanderers remain bottom.
Sydney got off to the perfect start with a helping hand with Wanderers keeper Ante Covic, who could only deflect a 10th-minute header from Marc Janko into his own net after the ball had bounced back off the crossbar and into his path.
It got worse for the home side in the 18th minute when marquee man Janko stabbed home his 11th goal of the season off the post to lead the A-League scoring charts after Chris Naumoff's weaving run had created havoc in the Wanderers box.
The irrepressible Janko pounced again in the 24th minute to leave th Wanderers in disarray when he zeroed in on a long ball from Sebastian Ryall and took advantage of a poor touch from stand-in stopper Brendan Hamill to clinically sweep the ball past Covic to make it a round dozen for the season.
It should have been four in the 27th minute but skipper Alex Brosque and Naumoff overcooked the opening, with the latter firing wide with Covic off his line.
Hamill made amends in the 32nd minute, heading a Yojiro Takahagi free-kick back across the face of goal for the lurking Iacopo La Rocca to plant the ball high into the net to give the Wanderers a glimmer of hope.
And Tony Popovic's men, who only arrived back in the country on Friday after their AFC Champions League win against Kashima Antlers, pulled another one back in the 42nd minute when Nikita Rukavytska got in behind the Sky Blues defence and squared the ball for debutant Kerem Bulut to fire into empty net.
And Bulut became the Wanderers hero in the 53rd minute as he latched onto a flicked pass from Mark Bridge to fire off a 20-metre drive into the far corner of Vedran Jetjetovic's net for a stunning equaliser.
But the Sky Blues were ahead again in the 75th minute when Antonis took advantage of hesitancy from Hamill to skip round the defender and send a low left-footed shot past a diving Covic.
But the plot thickened again in the 82nd minute when the Sky Blues had Tavares sent off after he picked up a second yellow card.
And it took a string of late saves from Janjetovic to keep Sydney's lead intact.
Sydney coach Graham Arnold said: "What a crazy game. We were 3-0 and had a great chance for 4-0 to have the game dead and burried.
"You have to give full credit to the Wanderers, they showed what Tony Popovic is made of. The team is always similar to their coach and they fought extremely well."
But Arnold insisted he never feared the game would get away from them.
"That's the benefit of having Antonis and Smetlz to come on," he said. "I was always confident of winning the game."
Popovic admitted his side were heartbroken to have finished without a point.
"Every defeat is painful but losing to your local rival is never easy to take," he said.
"That's three games we've had chances to win against them and should have won. But we walk way with no wins."
He praised 23-year-old new recruit Bulut.
"I'm delighted for him to get two goals but I'm disappointed they weren't in a winning team."
