For Southampton, nothing was more satisfying than the sight of Mauricio Pochettino hopping up and down on the touchline as Tottenham Hotspur’s final attack petered out. It is almost five years since they introduced Pochettino’s gifts to English football and their gradual decline has been dispiriting to watch. Yet this gutsy performance was a reminder of happier times, filling Southampton with hope in their fight against relegation, and they took pride from making their former manager let out his frustration so visibly at the end of this absorbing game.

If there was a disappointment for Mauricio Pellegrino after weeks of mounting speculation over his future, it was that Harry Kane’s 99th Premier League goal denied his team a first league win in 11 matches, keeping them in 18th place with 14 matches left this season. They might have nicked it when Michael Obafemi, a 17-year-old striker, spurned a glorious opportunity to score on his debut after replacing Manolo Gabbiadini in the 82nd minute. Yet it spoke volumes that Southampton’s efforts earned them applause from their crowd after the final whistle. Their commitment restricted Tottenham to few clear opportunities and they can be confident of staying up if they maintain this level.

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“We played against an amazing side, but I think we created problems,” Pellegrino said. “I think we are on the right path. I am sure we will improve. Obviously we are in trouble, but in three or four weeks everything can change.”

Pochettino agreed with his fellow Argentinian’s assessment of an even contest, refusing to make excuses despite a virus that depriving him of Hugo Lloris and Christian Eriksen and leaving many of his players feeling jaded in difficult conditions on the south coast. “We made a lot of mistakes in possession,” Pochettino said. “We gave them a lot of chances for transitions. The pitch wasn’t great, but it was the same for both teams.”

While Pellegrino’s default response to questions about his job security has been to point out that he is trying to lay the foundations for a brighter future at Southampton, his team’s early vigour gave the impression he is under no illusions about the rising culture of impatience in the Premier League’s packed lower reaches. Marco Silva’s sacking by Watford earlier in the day was a reminder of the insatiable desire for instant success and Pellegrino must have been heartened by the sight of his players tearing into their guests straight from kick-off.

The hosts were quick to the ball in midfield, with Mario Lemina catching the eye and Dusan Tadic’s sparking performance meant that they always had a threat in the wide areas. Southampton displayed an intent that has not always been evident under Pellegrino and it did not come against the run of play when they took an early lead.

Lloris’s absence unsettled Tottenham’s defence and Southampton had spotted that Serge Aurier can be guilty of questionable positioning. Aurier is an enterprising attacking force from right-back and his pace can get him out of tight spots, but the Ivorian was nowhere to be seen when Pierre-Emile Højbjerg almost set up Gabbiadini for a simple finish and he did not do enough to stop Ryan Bertrand from zipping a low cross across the slippery surface in the 15th minute. Gabbiadini was lurking again and the Italian’s presence forced Davinson Sánchez to slide and turn the ball past Michel Vorm, who was making his first start in the league this season.

However Southampton’s attempt to protect their advantage left much to be desired. Tottenham sought an instant response, with Eric Dier rapping the woodwork, and they were level when Kane peeled away from Jack Stephens to head Ben Davies’s corner past Alex McCarthy three minutes later. The thought occurred that Virgil van Dijk would have kept a tighter grip on the striker.

There was no stopping Kane once he had a yard on Stephens, though, and the sheer force of will that he displayed to meet Davies’s delivery underlined why reports of Real Madrid targeting the striker in the summer were dismissed so vociferously by Tottenham’s manager. “Again?” Pochettino said. “I am not going to speak about rumours. If I give a message to every rumour, I need to give my opinion at every press conference.”

The bigger concern for Pochettino was that Tottenham missed an opportunity to improve their hopes of finishing in the top four before games against Manchester United, Liverpool and Arsenal. Liverpool will go five points above them if they win at Swansea City on Monday.

Moussa Sissoko went close after meeting Davies’s driven cross, but Tottenham missed Eriksen’s craft. Dele Alli struggled to shoulder the creative burden and Son Heung-min did not have the beating of Cédric Soares.

Stephens’ last-ditch block denied Érik Lamela and Alli was inches away from turning in Kane’s cross-shot, but in truth Southampton endured few heart-in-mouth moments.