The home side ended leaders Auckland's six-game winning streak that started their life in the A-League Men but will be fuming after missing a golden opportunity to deal Steve Corica's charges their first defeat.
City youngster Medin Memeti scored in the 18th minute, just the second goal Auckland have conceded and the first time they have gone behind, before Guillermo May responded in the 53rd.
Auckland appeared to have taken the lead via Neyder Moreno in the 74th minute but the goal was contentiously chalked off for offside.
Five minutes later, Auckland goalkeeper Alex Paulsen failed to control Nando Pijnaker's strongly-hit backpass and watched in horror as the ball nestled in his own net.
But in the 95th minute, City goalkeeper Patrick Beach had a Moreno free kick go straight through his hands for the equaliser.
NIGHTMARE FOR AUCKLAND FC 😱 That is a seriously cruel bounce.— Isuzu UTE A-League (@aleaguemen) Moments after they had a goal disallowed, Alex Paulsen can't control Nando Pijnaker's back pass - and @MelbourneCity lead!Football is a crazy game.Watch #MCYvAKL live & exclusive on Paramount+. pic.twitter.com/qUKNULzpLMDecember 15, 2024
Auckland (19 points) lead Adelaide United (17), Melbourne Victory (16) and Aurelio Vidmar's City (13).
The result sets up a blockbuster Melbourne derby between Victory and City next Saturday, when Auckland will host Western United.
Auckland were without first-choice trio Dan Hall, Cam Howieson and Louis Verstraete through injury.
They had the first real chance when Jake Brimmer was cut down by Samuel Souprayen and skimmed the subsequent free kick over the bar in the 17th minute.
Less than a minute later, Cohen forced a strong diving save from Paulsen.
But Aziz Behich picked up the ball and slipped through Andreas Kuen, whose cross was coolly met by Memeti, who turned the shot home with the outside of his boot.
A mix-up between Auckland's keeper Alex Paulsen (pictured) and Nando Pijnaker gave City a 2-1 lead. (Morgan Hancock/AAP PHOTOS)
A lacklustre Auckland had just one shot on target at half-time.
But they responded after the break when May nodded home a Francis De Vries corner at the front post.
City's Steven Ugarkovic had the ball in the back of the net in the 68th minute but was narrowly offside.
Auckland then thought they had taken the lead when Moreno headed home a wonderful De Vries ball - only for it to be chalked off as Brimmer was offside in the build-up.
City took the lead through Pijnaker's own goal and looked set to claim a huge win until Beach failed to handle Moreno's late set piece.
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