Tottenham manager Ange Postecoglou insisted he would not relent from his philosophy of relentless attacking football despite facing the might of City with a mounting injury crisis and earned his reward.
Spurs captain Son Heung-min scored at both ends inside the opening 10 minutes.
Phil Foden put City in front before half-time, but Giovani Lo Celso levelled 20 minutes from time.
Jack Grealish restored the home side’s lead once more, only for Kulusevski’s header to ensure City have now dropped points in five of their last eight league games.
The English and European champions drop to third in the table, three points behind leaders Arsenal.
A point lifts Tottenham into fifth and snaps a run of three consecutive defeats.
The visitors’ daring approach was met with an early reward.
Son raced onto Kulusevski’s ball over the top and Ederson failed to prevent the South Korean from scoring his eighth goal against City.
The lead lasted only three minutes as Son cancelled his opener at the wrong end.
Julian Alvarez’s free-kick was flicked on by Erling Haaland and deflected off the unfortunate Son into his net.
Spurs started for the second consecutive game without a recognised centre-back and never looked capable of restricting City going forward.
Haaland missed what should have been a simple tap when he skewed wide after Tottenham coughed up possession inside their box.
City should have had the game out of sight before half-time.
Jeremy Doku smashed off the inside of the post before Alvarez also hit the woodwork from outside the box.
Haaland’s off day in front of goal went on as he blazed well over with another clear opening.
Yet, City did produce a move of clinical precision to go in front on 31 minutes.
Doku fed Alvarez inside the box and the Argentine squared for Foden to slot home.
Guglielmo Vicario was forced to make a stunning save from Bernardo Silva seconds into the second period to keep Tottenham in the game.
But City was then guilty of resting on their laurels and allowing Spurs’ makeshift defence some respite.
Lo Celso has been handed a rare run in the starting line-up by an injury to James Maddison and fired in off the post for his second goal in as many games.
Tottenham’s determination to play out from the back looked to have cost them 10 minutes from time.
Rodri robbed Yves Bissouma and played in Haaland, who crossed for Grealish to tap home.
But the drama was far from over.
Kulusevski timed his run perfectly to head in Brennan Johnson’s cross.
And City were incensed in stoppage time when referee Simon Hooper inexplicably stopped the game to award the home side a free-kick when Grealish was clean through on goal.
City’s punishment did not end there as yellow cards for Rodri and Grealish mean they will be suspended on Wednesday for a trip to an Aston Villa side that has won 13 consecutive home Premier League games.
AFP