Tottenham had threatened to win this Carabao Cup tie at a canter. Two goals up after 25 minutes, there was almost disbelief within the home crowd and not only because Timo Werner had scored the first.

Everybody knew this was not how the story would go and so we had the Manchester City fightback, Matheus Nunes scoring before half-time and then a concerted attempt by Spurs to seal the deal. They created a fistful of chances in the second half, some of them crystal clear, and yet they could not take them.

When Richarlison, on as a substitute, failed to finish from close range on 83 minutes, it felt obvious that City would have the opportunity to save their skins, to rescue a performance that did not reach the levels that Pep Guardiola demands.

They got it, the ball falling to the 19-year-old Nico O’Reilly after Guglielmo Vicario had flapped at a corner and the shot was goalbound only for Yves Bissouma, having come off the bench, to make the most dramatic of goalline clearances.

It was fiercely tense, Spurs putting their fans through the wringer because the fear had lurked even before Nunes’s goal, as the tide turned, that Ange Postecoglou’s team could throw it away.

Perhaps that was why the celebrations were so raucous when the six minutes of stoppage time were up, the music blaring, everybody dancing. They played the Abba song for Dejan Kulusevski because he had been excellent, the driving force.

Spurs had done it. They had the result to energise their season, their self-belief and it was one they deserved, however difficult they made it for themselves. On Sunday, they plumbed the depths in defeat at Crystal Palace, their worst performance of the season. Here the positive emotions surged. Could a trophy finally be on for them?

Both Postecoglou and Guardiola made changes, although neither of the lineups could be described as weakened, and the former lost Micky van de Ven to a hamstring issue on 13 minutes; he was not the only player to sustain an injury. By then, though, Spurs were a goal to the good, Werner scoring his first of the season after a Brennan Johnson-sparked break and a lovely low cross by Kulusevski.

Guardiola started with Phil Foden in the No 9 role, James McAtee working off him and it was strange to see City early on struggling to join their passes. Ilkay Gündogan missed one to John Stones on the edge of his area and was fortunate that Werner shot straight at Stefan Ortega.

It was nosebleed territory for Spurs midway through the first half when Pape Sarr made it 2-0. Kulusevski worked a short corner with Werner and Sarr started his long-range curler well outside the near post. To Ortega’s surprise, the midfielder was able to bring the ball back inside it at the last moment. The technique was wonderful.

At which point Spurs stopped doing what they had previously done, sinking back, making errors. City started to dig out their footholds. They created chances. Nunes almost found Foden after outpacing Archie Gray. Foden volleyed high after another Nunes ball.

There were groans from the home crowd when four minutes of stoppage time were signalled. Foden had just lifted a free-kick off target after Destiny Udogie, on as a Spurs substitute, turned into trouble. It was as if they knew what was coming. It did when Savinho beat Udogie to cross and Nunes was all alone at the far post.

Postecoglou knew his team had to bring greater energy at the beginning of the second half and they did. They got in repeatedly behind City’s high last line before the hour and yet the cushion of a third goal eluded them.

The South Stand had chanted during the first half that “Timo Werner scores when he wants”. They know it is not true. Werner wasted a one-on-one with Ortega and wafted another chance high. Johnson had extended Ortega and the goalkeeper would also throw out a hand to thwart Kulusevski as he ran clear up the inside right.

Spurs endured another injury blow when Cristian Romero was forced off while City, having lost Manuel Akanji in the warm-up, saw Savinho taken away on a stretcher after an awkward fall. On came the 19-year-old Jacob Wright.

Spurs lost Werner to a groin problem and they had to deal with the knowledge that they ought to have been out of sight; one flash from City could ruin it all. Wright almost provided it. He took an assured touch on the edge of the area and bent his shot inches past the post. It was close. O’Reilly went closer. City will have to look elsewhere for silverware this season.

“The news is not that we lost but for how long we didn’t lose,” Guardiola said. “It [the last time] was the FA Cup final [against Manchester United last season] and we were a bit hungover. I don’t like to lose but this competition is a bit different.”