Both teams found the net in time added on at the end of the match.
The visitors broke the deadlock on 66 minutes through Neyder Moreno after a tense opening period and looked set to claim maximum points and snatch top spot.
But a double off the bench from Archie Goodwin in the 81st and 95th minutes had the Reds just moments away from clinching a come-from-behind win.
But in one final twist, the visitors' Logan Rogerson headed in an equaliser in the 10th minute of time added on.
Despite coughing up a last-minute equaliser, Reds coach Carl Veart praised his troops.
"It's disappointing to concede so late," he said. "But proud of the boys tonight, it was a very tough test for them."
Both sides looked to gain the ascendancy after the early exchanges with the best chance arriving in the 21st minute.
Dylan Pierias came close to scoring for Adelaide United and was denied by keeper Alex Paulsen. (Matt Turner/AAP PHOTOS)
Auckland's Dylan Pierias was found in space out wide on the right and the full back drove towards the byline before firing in a cross which went dangerously close to sneaking in, forcing Alex Paulsen to swat away.
Five minutes after the restart and home keeper Ethan Cox was called into action. An out swinging corner from Francis De Vries was met by Nando Pijnaker who rose highest and powered a header towards goal, but it was expertly tipped over.
In the 64th minute, Jonny Yull delivered a free kick from on the right which eluded everyone in the area except Stefan Mauk, who was left unguarded at the back post.
The Reds midfielder controlled the ball before unleashing a half volley that rattled the cross bar.
Almost immediately after, the visitors thought they had taken the lead through substitute Neyder Moreno, who was slipped through by fellow substitute Jake Brimmer after United coughed up possession in the centre of the pitch.
Moreno was met by a tackle from Bart Vriends, but the ricochet fell perfectly for the Columbian who cooly dispatched the loose ball past Cox.
The referee's assistant raised his flag and after a momentarily delay and check from VAR, the goal stood.
In the 82nd minute the Reds equalised when substitutes Yaya Dukuly and Goodwin combined. Dukuly burst past Callan Elliot on the left wing before looking for his teammate who made his run into the box.
The pass made its way past the legs of Pijnaker to Goodwin, who tucked his shot away from close range.
VAR intervened again and referee Alex King was called over to adjudicate whether Dukuly had tangled with Elliot, but the contact was not deemed strong enough to overturn the goal.
Goodwin completed his brace deep into stoppage time and looked to have secured a win for Adelaide when he tapped in from five metres.
Then 10 minutes into stoppage time, De Vries whipped in a corner which was met by Rogerson at the near post to deny the hosts full points.
Auckland coach Steve Corica felt his side should have ended the clash with a win.
"I think we deserved a point, if not all three points tonight," he said.
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