Centre-back Hayden Matthews appeared to have scored his first A-League Men goal in the 83rd minute, after a resolute defensive performance, to give the Sky Blues a crucial away win at Go Media Stadium.
But after a lengthy VAR review, the goal was contentiously chalked off for offside, seemingly by Patryk Klimala in the build-up.
The extra time created by the review ultimately proved Sydney's undoing.
In the 97th minute, Jake Brimmer whipped in a free kick and Auckland centre-back Nando Pijnaker headed the ball to ground then backheeled it over the line.
Steve Corica's Auckland held on in the final three minutes of stoppage time to ensure a second consecutive win from as many games for the expansion club.
Sydney coach Ufuk Talay was understandably fuming after the disallowed goal while he will also have to consider his mounting injury list.
Costa didn't play Sunday's game  after he was substituted with hamstring tightness in Wednesday night's 2-1 Asian Champions League Two away loss to Japanese club Sanfrecce Hiroshima.
On Sunday, Lolley was assisted from the pitch after just 35 minutes with an apparent groin injury and replaced by Patrick Wood.
Hollman had treatment on his ankle in the first half and made way early in the second.
Auckland had the better of the early chances and should have taken the lead when Felipe Gallegos brilliantly slipped through Liam Gillian in the 55th minute, but he inexplicably lifted the ball onto the crossbar.
Sydney were screaming for a penalty when Francis de Vries appeared to drag down Klimala inside the box in the 59th minute.
But strangely, neither referee Shaun Evans nor the VAR intervened.
Jordan Courtney-Perkins forced a brilliant save from Alex Paulsen just before Matthews' would-be goal.
Then, Auckland failed to clear their lines multiple times and Matthews turned Anas Ouahim's driving ball home.
Sydney were ecstatic before the goal was belatedly chalked off.
Then Pijnaker delivered Sydney's undoing.
Auckland travel to take on Wellington Phoenix in their first derby next Saturday while Sydney are away to Brisbane Roar on Friday.