The visitors looked on course for a comfortable victory as they raced to a 2-0 lead inside 24 minutes thanks to Mark Bridge's volley and an embarrassing own goal by goalkeeper Vedran Janjetovic.
But Corey Gameiro pulled one back right on half-time and further strikes Sasa Ognenovski and skipper Alex Brosque – after Vitor Saba was shown a straight red card – capped an amazing comeback.
The thrilling contest was played in front of 41,213 fans, Sydney’s biggest ever regular-season home crowd and the largest crowd of any code for a regular-season match.
Elsewhere, Wellington Phoenix also came from behind to beat Central Coast Mariners 2-1.
Tom Doyle's early own goal handed the hosts the advantage, but Michael McGlinchey levelled matters before the break with a close-range header after Jeremy Brockie's penalty had struck the crossbar.
Nathan Burns grabbed the winner in the 54th minute, smashing home from Brockie's header back across goal.
