Tottenham’s woes in this corner of London are well-established and well-documented. When they made this latest trip to Stamford Bridge, the statistics showed they had won just once since 1990 – a sequence of 40 matches in all competitions.

Never mind. They needed only a draw to effectively ensure their Premier League survival, to send West Ham down and draw a veil over this most wretched of seasons.

It was a night when the hope pulsed until the last. Chelsea led through goals from Enzo Fernández and Andrey Santos but Spurs rallied, Richarlison scoring on 74 minutes to set up the grandstand finale.

Spurs threw everything at Chelsea, who needed a win to advance their claim on a Europa League berth. There were chances and there was drama; controversy, too. Micky van de Ven wanted a penalty when he was fouled inside the Chelsea area on a corner only the offence took place before the ball was in play.

It was too little, too late from Spurs and their fate will now be decided on the final day on Sunday when they welcome Everton to their stadium, where they have the joint-worst home record in the division. They may still need a point to stay in it. The nightmare is not over.

Spurs could not have imagined the bleakness to come for them at this venue when they won here in the old first division 36 years ago, Gary Lineker scoring the decisive goal for 2-1 in the 88th minute. De Zerbi did not run from the record; he addressed it with his players on Monday. It was not about history, he had said; rather showing up with spirit and energy.

De Zerbi worked with a clutch of Chelsea players during his time at Brighton, although two of them – Levi Colwill and João Pedro – were not in the squad on this occasion. The other two were in from the off – Robert Sánchez and Moisés Caicedo – as Calum McFarlane reverted to a 4-2-3-1 system.

The caretaker manager asked Fernández to work off the left wing and it was the Argentinian who made the breakthrough in the 18th minute. It was a clean hit from 25 yards, the ball wobbling and fading to the right of Antonin Kinský. In the heat of the moment, it looked getable for the Spurs goalkeeper. He appeared to pick it up a little late and was slow to get across. The ball was not flush in the corner.

A few minutes earlier, Kinsky had pushed a Cole Palmer curler out for a corner and the Fernández goal was a body blow for Spurs, as they had started brightly, fizzing their passes. Mathys Tel hit the near post with a header on 11 minutes from a teasing Pedro Porro cross.

Chelsea were the better team in the first half, the pendulum swinging sharply. Fernández drifted inside, which allowed Marc Cucurella to overlap. Porro was booked for a late one on Cucurella and Fernández whipped the free-kick from a tight angle out on the left for the near, top corner. It was a vicious effort, beating Kinsky only to come back off the crossbar.

Spurs’ early promise evaporated and there were frustrating final actions from Randal Kolo Muani and Tel. Chelsea hunted for a second before the interval. Kevin Danso made an important last-man tackle on Liam Delap. Palmer dragged an effort wide after errors by João Palhinha and Rodrigo Bentancur. There was needle, too, some of it involving Conor Gallagher, the former Chelsea midfielder, whose every touch was booed by the crowd that once adored him.

It is always fun to watch De Zerbi on the touchline; to listen to him – especially if you speak Italian. He felt the passions swirl because never mind Chelsea’s European aspirations, it was plainly a bigger game for Spurs. The travelling fans had made themselves heard in the early going and they got behind their players loudly in the early part of the second half.

They did not want their fate to remain the balance on the final day. It was all or nothing for them here. Their Chelsea counterparts were far more laid back. They could actually enjoy this.

Spurs played on the front foot after the restart. The question concerned their ability to make something happen; to show any sort of cutting edge. Tel crossed for Richarlison only for the centre forward to head wide from in front of goal. Fortunately for him, he was offside. Shortly afterwards, Richarlison headed at goal from a Porro corner. The effort lacked power.

De Zerbi had to change it but before he could get his substitutes on – including James Maddison – Chelsea went further ahead. It was a loose pass from Kolo Muani to Palmer, Bentancur wrong-footed, and Chelsea moved quickly up the right, Pedro Neto crossing, Fernández returning it from beyond the far post. Santos’s first-time finish was true.

Spurs fought back and it was an excellent move that led to their life-line – one of the substitutes, Pape Sarr, ending it with a lovely flick for Richarlison, who converted from close-range.

It was a breathless finale. Maddison tiptoed through only to be stopped by an excellent Jorrel Hato challenge and then controversy. Cucurella wrestled Van de Ven to the ground on a corner, which could have been a penalty only the referee, Stuart Attwell, decided that the ball was not live.

Delap was booked for a swipe with an arm on the Spurs substitute, Djed Spence, and the seven minutes of added-time seemed to last an age. There was a chance for Maddison from a free-kick, which he blew and further flickers from Tel. Spurs could not make it happen.