Son Heung-min scored at both ends inside the first 10 minutes, initially firing the visitors ahead before inadvertently diverting a free-kick beyond goalkeeper Guglielmo Vicario.
Phil Foden’s cool finish just after the half hour was cancelled out by a superb strike from Giovani Lo Celso before Jack Grealish looked to have swept home the winner 10 minutes from time.
However, Spurs refused to throw in the towel and Kulusevski’s towering late header earned Ange Postecoglou’s side a point.
Trent Alexander-Arnold scored an 88th-minute winner as Liverpool staged a dramatic late fightback to beat Fulham 4-3 at Anfield.
Alexander-Arnold had helped Liverpool open the scoring in the 20th minute when his free-kick hit the bar and bounced in off Fulham goalkeeper Bernd Leno, only for Harry Wilson to swiftly equalise.
Alexis Mac Allister restored the home side’s lead with a stunning long-range effort, but Kenny Tete equalised in first-half stoppage time and Bobby De Cordova-Reid headed the Cottagers into the lead 10 minutes from time.
However, Wataru Endo scored his first Premier League goal to make it 3-3 after 87 minutes and Alexander-Arnold completed the remarkable turnaround seconds later.
Enzo Fernandez scored twice as 10-man Chelsea held on to beat Brighton 3-2 at Stamford Bridge.
Headers from Fernandez and Levi Colwill gave Mauricio Pochettino’s side an early two-goal lead, but Facundo Buonanotte reduced the deficit moments before Conor Gallagher was shown a second yellow card for fouling Billy Gilmour in first-half stoppage time.
Fernandez restored Chelsea’s two-goal lead from the penalty spot midway through the second half before substitute Joao Pedro’s late header set up a tense finish.
Ollie Watkins scored a 90th-minute equaliser as Aston Villa twice came from behind to draw 2-2 with Bournemouth at the Vitality Stadium.
Antoine Semenyo’s early goal was cancelled out by Leon Bailey after 20 minutes and, although Dominic Solanke put Bournemouth ahead again early in the second half, Watkins’ late header ensured the spoils were shared.
West Ham and Crystal Palace also had to settle for a point each at the London Stadium, where Mohammed Kudus opened the scoring for the home side after 13 minutes.
However, the visitors were gifted an equaliser early in the second half when Odsonne Edouard capitalised on a poor back pass from Konstantinos Mavropanos to slot the ball beyond Alphonse Areola.
