What was it like to be at that wedding in Cana when the water was turned into wine? How did it feel to be in Smyrna when the flames refused to consume the body of St Polycarp? Do the holy waters of Lourdes really cure the lame? Miracles, it turns out, can happen, and the Tottenham Hotspur Stadium witnessed one of the most improbable there has ever been: Timo Werner scored.

And so Tottenham, not for the first time recently, got away with it.

Related: Luton Town v Aston Villa: Premier League – live

They had fallen behind to Eberechi Eze just before the hour, but Werner’s first goal for the club followed in quick succession by a Cristian Romero header and a neat finish from Son Heung-min gave them a win that keeps the pressure on Aston Villa in fourth and increased their lead over Manchester United to six points before Sunday’s Manchester derby.

But it was a close-run thing and Oliver Glasner can feel that, with performances like this, relegation should not really be a threat for Crystal Palace. The shape may have been Glasner’s preferred 3-4-2-1 rather than Roy Hodgson’s back four, but the approach will have been comfortingly familiar to Palace: let the opposition have the ball, keep it tight and look to pinch something on the counterattack. In the end, they had only 20% possession.

“We did a great job for 60-70 minutes,” said Glasner. “We stuck to the plan and defended well. We could have been more confident in possession.”

That is 19 goals Palace have conceded in the last 15 minutes of games this season. For Spurs, the pizzazz of the early part of the campaign has gone.

Palace were diligent and Spurs could not get going in a first half when the only opportunity was one of those that somehow makes the scoring of a goal seem a feat of implausible difficulty – in other words it fell to Werner.

There is something agonising about watching the German in the contemplation of a chance. The shoulders stiffen, the stride becomes a little tighter, a sense of unease descends upon the stadium. He is the man who, midway through signing a stack of Christmas cards, suddenly finds the pen sticking as he attempts to write his own name, enduring an awful mental glitch as the capacity to do something that ought to be second nature deserts him.

The longer Werner has to think about it, the worse it is and when he was released by Son after 20 minutes, he had a long, long time to think about it. Werner had run from inside his own half, charged on, drifted right, seemed as though he might have gone past Sam Johnstone only for the keeper to scramble across to block. Good goalkeeping, yes, but that was Werner’s 12th shot in his fifth league start since joining on loan from RB Leipzig in January. None of them had brought a goal.

“Timo missed the chance in the first half,” said Ange Postecoglou, “but he was a constant threat to them. Goals make them feel better and a bit more confident and this relieves the pressure but he was really aggressive with his running and, apart from the missed chance, his general play was really good.”

Although Son clipped a shot against a post early in the second half, Spurs fell behind after 59 minutes. Palace have missed Eze this season. It was his forward surge that drew the free-kick that he then flashed into the top corner. It was a high-quality strike, his sixth goal of the season, but there must be questions about the position of Guglielmo Vicario in relation to his wall, with neither seemingly covering the right of the goal.

With 13 minutes remaining, it happened. Brennan Johnson wobbled in from the right, crossed low, and Werner, with little time to think and few options, knocked the ball into a gaping net. The sun pierced the clouds, and joy abounded in north London.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

Romero nodded in James Madison’s lobbed cross to put Spurs ahead soon after before Son made the game safe with a well-worked counter.

It was not the most convincing win, but nobody will remember that in years to come. This was the day Timo Werner scored.