It may be a cliche but sometimes football really is a game of two halves. How else to explain what took place on a wild afternoon on the south coast as Southampton staged a remarkable comeback to clinch a victory that will be spoken about in these parts for some time and has surely injected Ralph Husenhüttl’s side with the belief they can, and will, avoid relegation.

That much could be taken from the scenes at the final whistle. The home crowd were on their feet in rapturous applause as Southampton’s players formed a huddle. They looked like men who had just gone to war and, to some extent, they had. Battered by Tottenham during a one-sided first period, the hosts played the second half with a relentless determination to cancel out Harry Kane’s goal on 26 minutes.

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And ultimately they were successful as Yan Valery equalised and James Ward-Prowse struck the winner with a curling free-kick nine minutes from full time.

Cue bedlam in the stands and, in the directors’ box, a sense of shock and fury within the Argentinian who used to be the main man here. Serving the first instalment of a two-game touchline ban for improper conduct, Mauricio Pochettino could only look on as his current club wilted against his former one. He later accused his players of arrogance and the bigger picture is that, having qualified for the quarter-finals of the Champions League with victory over Borussia Dortmund, Spurs may not qualify for next season’s edition of the competition via their league position. They remain third but are now only three points ahead of Manchester United in fourth and four ahead of Arsenal in fifth, before their meeting on Sunday, and have played a game more than both sides.

“A lot of people will now realise our real level,” said Pochettino, but the truth is nobody really does. After all, this is a team that can deliver two incredibly impressive displays against the leaders of the Bundesliga and, within the same period, lose at Burnley and Southampton. It must be a maddening state of affairs for those who filled the away end here.

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By the end it felt like a trick of the mind to remember just how Tottenham dominated territory and possession in the first half via assured movement and incisive passing. Their defence were rarely troubled while in midfield Dele Alli simply picked up from where he had left off in his first appearance since sustaining a hamstring injury in late January.

In attack Kane was a constant menace and scored his 200th career goal with a composed finish following a slick exchange of passes with Alli, albeit the England captain appeared to be marginally offside when he struck.

It was comfortable for the visitors and while Pochettino stayed in text-message contact with his coaching staff below, led by assistant Jesus Perez, there was little to worry him. In truth the 47-year-old could have kept his phone in his pocket.

Southampton ended the first half not having had a single shot on target. They looked beaten. But then came the break and a crucial double substitution by Hasenhüttl. On came Shane Long and Josh Sims for Oriol Romeu and Charlie Austin and suddenly the hosts were playing with more drive and energy, causing panic in Tottenham’s defensive ranks.

And it was that panic, allied to a general drop in intensity by the visitors, that led to Southampton’s equaliser. Stuart Armstong, on as a 73rd-minute substitute for Long after the striker sustained a hamstring injury, delivered a low cross that Davinson Sánchez and Jan Vertonghen both missed and Danny Rose allowed to run between his legs in the belief that nobody was behind him.

But someone was – Valery, who struck from close range to secure his second goal in two games following his stunning strike against Manchester United last week.

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Tottenham were increasingly out of ideas in attack and all over the place in defence, summed up by the moment Kyle Walker-Peters clipped Armstrong as he drove forward. The full-back was booked by Kevin Friend, which sparked outrage in Armstrong as he pointed out to the referee that he was clear on goal. But the Scotland international was celebrating soon after when Ward-Prowse, located by the D of Spurs’s area, arched the subsequent set piece past Hugo Lloris.

“That was the best second half since I’ve been here,” said Hasenhüttl as he reflected on a win that lifts Southampton to 16th, two points above the drop zone. They have hope.

For Tottenham, who were somewhat lucky not to lose Moussa Sissoko to a late red card after he thrust his head at Nathan Redmond, comes another period of introspection.