Mariners forward Wurigumula had her penalty in the eighth minute of stoppage time saved by Jada Whyman, but the Chinese international slotted the loose ball home to secure the visiting team's victory.
It was the final decisive act of a match that ended in third-placed Sydney's first defeat in eight games and sent the Mariners soaring five places on the ladder to fourth.
Sydney looked to have salvaged a point in the second minute of added time when a Mackenzie Hawkesby free-kick from over 30 metres squirmed through the hands of makeshift goalkeeper Ash Irwin.
Earlier, in the 34th minute, the visitors opened the scoring when a cross from Jazmin Wardlaw cannoned off Sydney defender Charlotte Mclean and beat Whyman.
The Mariners substituted starting goalkeeper Casey Dumont at half-time after a knee issue, but her replacement Sarah Langman was sent off in the 78th minute.
Langman, who had already received a yellow card for time wasting, collected another and was shown a red after she tripped Sydney substitute Abbey Lemon outside the penalty area.
Defender Irwin took over the goalkeeping duties and immediately dropped the free-kick given for Langman's foul and the ball was turned into the net by Sydney's Tori Tumeth.
However, Tumeth was adjudged to have fouled the Mariners third custodian of the night.
Tumeth was also involved in the final twist of the night when referee Bec Mackie awarded a penalty after spotting the ball had come off the defender's boot onto her hand.
Wurigumala slotted in the revbound to secure maximum points.
Central Coast strung together more passes in the first half but Sydney had five shots to one on target before the break, with Dumont making a number of comfortable saves.
Tom Whiteside, who was standing in as Sydney head coach for the suspended Ante Juric, brought on Matildas forward Cortnee Vine for the second half.
Vine added some urgency but Sydney still struggled to create clear cut chances against a Mariners side who defended with composure and looked threatening going forward.
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