Wellington fell 2-0 down to the Mariners to goals from Nick Fitzgerald and Eddy Bosnar.
However, a stirring second-half comeback was sparked by Roly Bonevacia and completed by Kenny Cunningham's double - including a 95th-minute winner.
Kicking off after Wellington's thriller, Sydney knew they would drop out of the top two if they failed to claim three points.
Enver Alivodic put the Jets into an early lead, but Sydney roared back to go 3-1 up by the 56th minute.
However, Sydney-bound winger Andrew Hoole set up Edson Montano before netting a goal of his own from the penalty spot to level the scores once again as Sydney fans watched on aghast.
There was still time for one last twist as Jets keeper Ben Kennedy failed to collect a cross and Sky Blues striker Shane Smeltz headed the ball across the face of goal. Substitute winger Robert Stambolziev reacted first and slotted the ball home from close range.
Sydney are level on points with table-toppers Melbourne Victory, who face Brisbane Roar on Saturday, with Wellington a point back in third.
