Once again Tottenham Hotspur were in the last chance saloon against Chelsea. Lose on Wednesday and the damage to their Premier League title hopes would most likely have been fatal. This time, however, it did not descend into the equivalent of one of those scenes in which bodies are hurled across the tables and gunfire shatters the whisky bottles. Tottenham kept their cool and the 2-0 home win was notable for its comfort in the closing stages.

“It was not the first time we have played well against Chelsea,” Mousa Dembélé said. “But this time when we went in front, we did not panic. That was very important and it was the difference to the previous times we had played them. When we went in front in those games, we tried to change the way we were playing – we wanted to battle. But this time, we kept to our game and we played like adults. We were very relaxed.”

Dembélé is one of the more laid-back characters in English football but it is stating the obvious to say that he was anything but in the now notorious fixture at Stamford Bridge last May. Tottenham needed to win in order to keep their title hopes alive yet they threw away a 2-0 lead to draw 2-2 and confirm Leicester City as champions. Spurs lost their composure completely that night and one of the symbols of the meltdown was provided by Dembélé, when he poked Chelsea’s Diego Costa in the eye just before half-time. Dembélé would be banned for six matches. Tottenham were 2-0 up at the time.

They were also 1-0 up at Stamford Bridge in the league fixture earlier this season, in November, only to concede in first-half stoppage time and be reeled in during the second half. Chelsea won 2-1 and a positive opening 45 minutes for Tottenham counted for nothing in terms of points.

The reference for the game on Wednesday was the Battle of the Bridge, whether Mauricio Pochettino liked it or not. The Tottenham manager had tried to play down its significance in the buildup to the fixture but even he found himself referring to it afterwards. The Argentinian talked about how it had been “tough at the end of last season – in different games, we missed how to be more competitive, to compete in a better way”. The Chelsea game was one of them and, by competing in a better way, Pochettino meant remaining focused and disciplined; hanging in during the moments when high-quality opponents have the upper hand.

It is known as game management or, simply, maturity. Tottenham showed they had it; that they had learned lessons from last May, after Dele Alli’s second goal of the evening in the 54th minute. There was still time for a Chelsea comeback, similar to last season, and there were frayed nerves and simmering tensions.

Nothing boiled over. Tottenham did not go looking for fights, nor did they allow themselves to be sucked in to anything. Cesc Fàbregas, the agent provocateur in Tottenham’s eyes from last May, came on as a 79th‑minute substitute to boos but he was no red rag. At 2-0, Chelsea barely threatened. Pochettino’s team have now won five matches in succession to climb to third place in the table.

“We have matured,” Dembélé said. “We are now another year together. Dele is in his second season with us and is growing all the time. All the team now know each other more, and the manager, as well. This was a very important win for us. If we hadn’t won, Chelsea would have been very difficult to catch.”

Alli is on fire. He has scored seven goals in his last four appearances and his licence to roam against Chelsea from his position off the striker, Harry Kane, in Pochettino’s 3-4-2-1 formation was particularly noticeable. At times Alli played like a second striker and the way that he timed his runs into the six-yard box to score twice with his head was extremely encouraging.

Alli is merely one example of Tottenham’s burgeoning confidence. Christian Eriksen looks reborn after the low point of the Champions League exit at Monaco on 22 November and what Victor Wanyama, the summer signing from Southampton, might lack in refinement on the ball he makes up for in midfield enforcement.

Goals from behind the striker are an essential ingredient to any title-winning team and Alli now has 10 in the league – which equals his return from last season. Son Heung‑min has contributed six; Eriksen five.

Pochettino’s philosophy, as he likes to call it, has long been clear and the squad that he has assembled are on board with it. Moreover, he has shown this season that he has a tactical plan B, with his three at the back, and even a plan C, if his 4-1-4-1 formation is taken into account. The 4-2-3-1 had previously been his default system.

He has started with three at the back on five occasions – once last season; four this time out – and has won on four of them, with the other being the 1-1 draw at Arsenal in November. The approach gives him a balance between security at the back and options going forward, where the wing-backs Kyle Walker and Danny Rose can press even higher up the pitch.

Pochettino seems to be getting more confident and decisive and the overall impression is one of optimism and a club moving in the right direction. Two of Tottenham’s next five league games are at Manchester City and Liverpool. They scent opportunity.

“With the quality we have, we can achieve whatever we want,” Dembélé said. “Last year we showed we are moving towards doing something and this year, who knows? We are playing very well and we are confident we can go on a good run. Anything is possible. I was ready to win silverware last season – we are even more ready now.”