The strange thing was that Roberto De Zerbi, always such a livewire in his technical area, barely flinched. The Brighton manager had seen Pervis Estupiñán, on as a substitute, sculpt a masterpiece from long-range to put his team 3-0 up just after the hour.

Perhaps, it was simply a reflection of De Zerbi’s comfort. Because at that point, it was easy to write that Brighton had been outstanding, Tottenham outclassed. Brighton wanted to find a spark in the Premier League, having saved most of their best stuff this season for their Europa League adventure. How they found it.

Related: Brighton v Tottenham: Premier League – live

Estupiñán had taken a couple of touches to set himself after James Milner’s short corner and the shot was angled beautifully into the far top corner, Guglielmo Vicario helpless in the Spurs goal. It was of a piece with the Brighton performance. Jack Hinshelwood and João Pedro had scored their first-half goals and there would be more, another penalty from the excellent Pedro after a foul by one substitute on another – Giovani Lo Celso on Evan Ferguson.

The truly crazy thing was that Brighton were left to hang on a little at the end after they completely stopped playing. Tottenham scored one, then another and they advertised further damage. They couldn’t, could they?

The thought certainly flickered through the minds of the Brighton support when Pierre-Emile Højbjerg hit the post in the fifth of nine additional minutes and Pedro Porro’s follow-up was deflected narrowly wide by Estupiñán. De Zerbi was animated now, all right.

The improbable comeback had been sparked by the Spurs substitute Alejo Véliz on 81 minutes, his first goal for the club swept home after Dejan Kulusevski had robbed Lewis Dunk and Son Heung-min crossed low. Kulusevski was caught horribly by Dunk in the act of winning the ball; Dunk was booked and will be banned for the trip to West Ham on Tuesday.

Ben Davies made it 4-2 with a header after Spurs had worked a short corner and it really was extraordinary to see how much they created thereafter, at least four decent openings. Where was this kind of fight and pace, previously? Spurs had not been this poor, this outclassed under Ange Postecoglou. Now they threatened to rise like a phoenix, mainly through the sheer force of their collective will. Yet it ought not to deflect from what had gone before. And it was a lot.

It was Brighton who imposed themselves at the outset and continued to do so, a blur of blue and white, of shifting shapes and they were full value for their two-goal half-time lead. The truth was that they should have been out of sight.

Vicario had made it clear that it would take something special to beat him, as he stood tall to deny Danny Welbeck twice in the early running; the second was a fine stop. Hinshelwood provided it.

The move for the breakthrough was fired by Pedro, who burst from left to right, across the edge of the Spurs box, slaloming away from a series of challenges. The visiting defenders were sucked towards him, there was space for Hinshelwood on the right and Pedro found him. The rest was all about the power and technique of the 18-year-old, his shot fizzing high into the roof of the net. Vicario barely had time to blink.

Brighton missed eight players through injury and two more were fit enough only for the bench, Estupiñán being one of them. You would not have known it. Their first-half fluency took the breath and Tottenham’s makeshift back four, featuring Emerson Royal and Davies in the middle, were given the runaround. They missed their injured defensive leader, Cristian Romero. Postecoglou was without eight other players.

Brighton made it 2-0 after a VAR check. It felt as though something was amiss in real time when Welbeck, well placed after a corner had broken to him, went down rather than get away his shot. When the replays started to roll, it was clear that Kulusevski had pulled his shirt. The Swede was booked and he will be suspended for the game against Bournemouth on Sunday. Pedro’s conversion from the spot bristled with assurance. Brighton had plenty more before the half-time whistle. Milner curled a shot against the far post, Facundo Buonanotte had the ball in the net only to be pulled back for offside and Vicario denied Pedro in a one-on-one after a loose Porro backpass.

Richarlison struck the outside of the post in the 45th minute after a Brennan Johnson pass but that was pretty much all that Spurs managed as an attacking force in the first half.

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As always, it was difficult to classify Brighton’s system, mainly because Buonanotte was everywhere until his substitution, a menace between the lines. The interchanges all over the pitch were so easy on the eye.

Tottenham worked hard to stop the bleeding in the early part of the second half. Destiny Udogie called Jason Steele into action after seeing an initial effort blocked by Jan Paul van Hecke and, briefly, Richarlison became the central figure.

The Spurs No 9 dragged one shot just wide and worked Steele only to have strayed offside. Shortly afterwards, he had the ball in the net only for the flag to go up again. He threw down his hands in frustration. It was not his night. Nor was it one for his team, despite the late madness.