A hard-earned, robust, counterpunching 1-0 win against the team who put six past us last month? It’s just who we are, mate. It is of course classic Angeball to kick and hassle opponents into errors, to irritate and snarl in midfield, and to find a ruthless edge just when it seemed that the first leg of this Carabao Cup semi-final was beginning to turn Liverpool’s way following the introduction of Trent Alexander-Arnold, Luis Díaz and Darwin Núñez after an hour of surprising ineptitude from the Premier League leaders.

This was a different Tottenham Hotspur from the one that collapsed against Arne Slot’s team 17 days ago. Implausibly, with Cristian Romero and Micky van de Ven still missing in central defence, there was snap and aggression from start to finish. There was Yves Bissouma, who walked a tightrope after an early booking, finding it within himself to dominate Liverpool’s midfield. There was Djed Spence filling in for Destiny Udogie and keeping Mohamed Salah quiet. And there was, perhaps only fleetingly, a sense that life remains in the Ange Postecoglou project, no matter how precarious it has felt for much of a trying campaign.

Related: Bergvall gives Tottenham edge in Carabao Cup semi-final to fury of Liverpool

Naturally Spurs put their manager through the full gamut of emotions. Postecoglou was animated by his standards here. There was even a very dramatic drop to the knees when Pedro Porro shot wide after an error from Alisson early in the second half. Had Postecoglou seen his team’s best chance come and go? Spurs being Spurs, it felt that way when Porro failed to capitalise on Alisson losing possession after being driven to distraction by Lucas Bergvall, who was both the best player on the pitch and very lucky not to have been sent off for a second yellow card shortly before his winning moment.

There were four minutes left when Bergvall fired in the only goal after Dominic Solanke rolled substitute Ibrahima Konaté, turned and laid the ball into the path of his team-mate. Liverpool raged, claiming that the 18-year-old midfielder should have been off after taking out Kostas Tsimikas before scoring his first goal for Spurs since joining last summer. Arne Slot would later note sarcastically that Postecoglou had grumbled about refereeing decisions after Spurs lost to Newcastle last weekend.

But take nothing away from Postecoglou. So often criticised for his gung-ho approach, this was a more resolute version of Spurs. They did not overcommit, their midfield setup was more conservative, they were not caught on the counterattack and, when it comes to whether Postecoglou’s insistence that he is building for the future should be taken seriously, it was hard to look beyond how this victory centred around the performances of players with their best years ahead of them.

It was not just Bergvall. Spence, 24, made the crowd roar when he jumped into a crunching tackle on Conor Bradley in the first half and there was a lovely moment after half-time, Archie Gray winning possession on the edge of the Spurs area, stepping out of central defence, gliding as he moved forward before releasing Dejan Kulusevski with a beautiful pass with the outside of his right foot.

Gray, remember, is 18. He is predominantly a midfielder, elegant and controlled, but is filling in at the back because of Spurs’ injury crisis.

Related: Bergvall gives Tottenham edge in Carabao Cup semi-final to fury of Liverpool

Mature beyond his years, Gray’s sacrifice sets an example. He was not overawed by marking Diogo Jota, who was not given a sniff of goal, and his excellence helped Antonin Kinsky, the 21-year-old Czech goalkeeper on his debut.

“I pray to God I’m the beneficiary of their talent,” Postecoglou said of the tyros. He raved about Gray and loved how Bergvall neutralised Ryan Gravenberch, Alexis Mac Allister and Curtis Jones. Liverpool, strangely underpowered, never got going. There were so many loose passes, so many heavy touches. Slot seemed bewildered.

Liverpool will expect to get the job done at Anfield in the second leg on 6 February. They still had enough moments in the final third. Alexander-Arnold, who began on the bench after his calamity against Manchester United, had a shot cleared off the line by Radu Dragusin. Núñez almost equalised with a volleyed flick, only for Kinsky to spring to his right and tip the ball wide.

There was hope for Spurs in that match-winning save from their new goalkeeper. Likened to Petr Cech, Kinsky only joined from Slavia Prague last weekend. Spurs have struggled since losing Guglielmo Vicario, with the 36-year-old Fraser Forster unable to adapt to Postecoglou’s demands to play out. They have a modern deputy now, and it was very Postecoglou to throw Kinsky straight in against Liverpool. Such bravery is why Spurs fans remain desperate for this to work.