Mauricio Pochettino has been at Tottenham Hotspur for only two and a half seasons but, already, he has plenty of history with Chelsea – and it goes deeper than the now notorious 2-2 draw at Stamford Bridge at the end of last season, when his team lost a lead, their heads and any chance of the title.

Pochettino can reflect on the 5-3 home win over them in his first season, which was one of the first indications that his side could play in the manner that he demanded while there would be the 2-0 Capital One Cup final defeat a couple of months later.

Earlier this season, there was the 2-1 defeat at Stamford Bridge, which Pochettino has continued to lament, although he does believe that it represented a turning point for this team. After the Champions League exit in Monaco a matter of days earlier, Pochettino detected the signs of his players getting their groove back.

Every meeting with the team from the west of the capital has seemed loaded with significance and this one was no different. Never mind that Chelsea were after the record for consecutive top-flight league wins. It was Tottenham for whom this was arguably the bigger game. Put it this way. Which team could most afford to lose? It was not Spurs.

Pochettino wanted to see a statement of intent from his players, rather than the completion of any revenge mission for the Battle of the Bridge and, thanks to the kid who cannot stop scoring, he got one.

Dele Alli’s goals were similar productions. They were created by the guile and delivery of Christian Eriksen and Alli finished each of them with his head. Moreover, on each occasion he ghosted in between César Azpilicueta and Victor Moses.

The 20-year-old has now scored seven times in his past four appearances for a tally of 11 in all competitions for the club season – which is one more than he finished with last term. The home support are fond of reminding everybody how they have got Alli. He strutted his stuff as though he owned White Hart Lane and there was a moment he will cherish when he was substituted on 86 minutes in the form of a rousing standing ovation. He even got a sporting handshake from David Luiz, the Chelsea defender.

Pochettino had stuck with the three-at-the-back strategy that he had used in the 4-1 win at Watford on New Year’s Day and the idea behind the 3-4-2-1 formation was to provide the platform for the full-backs, Kyle Walker and Danny Rose, to press high up the field, which they did to good effect. But it was also noticeable how much license Alli was given to roam in his role off the striker, Harry Kane.

Jan Vertonghen had been guilty of playing Eden Hazard onside in the early running for a big chance that the Chelsea winger lashed wide but Pochettino’s defence came to contain the threat of their opponents with relative comfort. And, further forward, Alli’s quest for the little spaces in the decisive areas would make the difference. Gareth Southgate, the England manager, looked on approvingly from the stands.

Tottenham jump to third in the table and, in the process, they have squeezed Arsenal out of the top four. Pochettino has now won four of the five games in which he has started with three at the back – the other one was the creditable draw at Arsenal in November – and it is getting to the point where it would be a surprise if he did not persist with the approach, much as Antonio Conte has done with his 3-4-3 at Chelsea.

Pochettino certainly has the personnel at his disposal, with Eric Dier’s adaptability on the right of the defensive three once again worthy of note and Victor Wanyama a towering presence in defensive midfield. Walker and Rose, meanwhile, continue to be influential. They won the battle of the wing-backs, pushing Moses and Marcos Alonso back.

What was striking was how Tottenham saw the game out after Alli’s second goal, when there were still 36 minutes to go. Pochettino and Conte had talked about how the Battle of the Bridge was behind them – a “closed chapter” to quote the former – but, with the Chelsea fans referencing it repeatedly in their chants, it felt as though there was plenty of carry over.

Rose, a central figure last May, was involved in a series of flashpoints, crunching in on his opponents and getting a bit back, as well, while in the first half there was the feeling of simmering tension. In other words, it was difficult to blot out the recent past.

The key detail of the 2-2 draw was how Tottenham had thrown away their 2-0 advantage in the final half hour or so but, on this occasion, their maturity was pronounced – and that was of great comfort to Pochettino. The closing stages were notable for how few scares there were in front of Hugo Lloris’s goal.

The evening became a celebration for the home support, and they told Pochettino at the end how they thought he was magic. His team are once again playing as they did in their better moments last season and it is remarkable how they are coming into form at around the same time. With Alli in this kind of touch, the optimism feels tangible.