Last Tuesday, Tottenham played Barcelona in the Camp Nou for a place in the Champions League knockout stages. On Wednesday, they face Arsenal in a League Cup semi-final. A game against Burnley in front of a half-full Wembley, rain sheeting down and adding an extra chill to an already freezing Saturday, was always going to be what advertising types call a tough sell.

Thank the lord then, for Christian Eriksen. For 90 minutes, it was the sort of grim afternoon that might lead everyone to question their life choices, the 0-0 scoreline to that point even less interesting than it might sound.

Tottenham are a different team when Eriksen is on the pitch: mostly that is for his invention and the way he seems to gently control games as if he is a delicate marionette operator, but this time it was his finishing. The Dane was brought on as a substitute to conjure something for a sluggish Spurs side, which he did just as second-half injury-time began, sweeping home his late winner and causing several Burnley players to sink to the turf. Cruel old game, football.

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Sean Dyche said that Burnley had been “done by a lump down the pitch”; a little uncharitable, perhaps, because one man’s lump is another’s controlled long pass, but it is true that his side had frustrated Tottenham with a 5-4-1 system and tactics you might call pragmatic.

“We limited them, by their standards,” said Dyche. “They had to work incredibly hard to get something.”

This is exactly the sort of game where it is smart to park the bus, against a tired team with bigger things on their mind and with a crowd already frustrated at having to show up at their rented home again, months after they thought they would be shot of the place.

At the moment Tottenham feel like one of those couples on Grand Designs who have to live in a caravan while their ambitious, self-sufficient eco-home with a £10,000 bath is dogged by delays. Admittedly, Wembley is an expensive and very well-appointed caravan, but the point is nobody wants to be here, the novelty wore off some time ago and everyone is grumpy.

Facebook Twitter Pinterest Joe Hart saves from Érik Lamela as Burnley threatened to derail Spurs’ pursuit of the top two. Photograph: Mike Hewitt/Getty Images

But while not many of the 41,645 in attendance will have enjoyed most of their afternoon, Mauricio Pochettino was delighted. “We know very well you need to play 90 minutes plus. I’m so happy because we played much better than the opponent. It would have been a frustrating afternoon if we hadn’t got the three points. For us, it was about having patience. The character and mentality of the team was amazing, to keep pushing. It was a massive effort to finish the week in that way.”

With those games either side of this one in mind, Pochettino made five changes, including giving the 18-year-old midfielder Oliver Skipp his full debut. “Fantastic. Fantastic,” Pochettino said about the youngster, who at first glance looks like the mid-point between Eric Dier and Harry Winks. “He played like a 30-year-old man. I said to him ‘You look so relaxed.’ That’s the difference between someone who’s going to be a top player against someone who was a normal player like me.”

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Perhaps because of the changes, perhaps because they have bigger fish to fry, Spurs lacked their usual intensity, looking like a team who just wanted to get this game out of the way; understandable perhaps, given the fixtures it came between, a little like asking someone to get excited about the tap water that arrives after the lobster and before the steak.

They struggled to make chances and squandered the ones they did create before Eriksen’s winner, most notably from Son Heung-min and Dele Alli in the closing stages, as that frustration almost graduated to desperation.

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But then arrived Eriksen, right at the end, scoring from a Harry Kane pass after the referee had waved play on following a foul on Alli. Eriksen saved Tottenham’s Champions League campaign with a late goal against Inter and while it might be a bit much to say this one has saved their title challenge, it at least keeps them in touch with Liverpool and Manchester City.

“We are in a very good position,” said Pochettino, celebrating his 100th Premier League win. “That is the reality: after 17 games, we have 39 points and are third in the table. It’s a massive achievement for us – we are there, we are close.

“Look at what happened in the Champions League. After three games we had only one point – nobody believed, but we believed it was possible. The most important thing in football is belief and faith and if you give 100% all can happen.”