With six minutes remaining, Alan Pardew was celebrating on the touchline. At the final whistle, the Crystal Palace manager looked shellshocked and wore the haunted look of a man who knows that he is hanging on to his job by his fingertips after an extraordinary match delivered an improbable Swansea City victory.

Palace had seemingly come back from the dead when they scored three times in nine minutes to take the lead after trailing 3-1, with Christian Benteke’s late goal prompting some Swansea fans to head for the exits, resigned to defeat as well as relegation.

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The cheers from afar moments later would have told them that something remarkable was happening as Fernando Llorente, who has struggled so much since his arrival from Sevilla in the summer, scored twice in injury time to breathe new life into Swansea’s season and inflict a sixth successive defeat on a Palace side that are now only outside the relegation zone on goal difference.

Pardew looked a broken man, flabbergasted and furious with the way that his fragile defence imploded yet again. They have now gone 18 Premier League games without keeping a clean sheet and Pardew clearly underestimated their inadequacies beforehand when, alluding to their problems in that department, the manager talked about how he “couldn’t see us winning at Swansea unless we get two goals”. Little did he realise that they would need six.

The question now is how patient the Palace board will be with a manager who is in charge of a club that has the worst record across all four divisions in the calendar year. Not only that, but he seems unable to arrest the decline. “That’s not my decision,” Pardew said when asked whether he thought the board would back him. “My decision is always the same; when you’re a football manager you’ve just got to try and address the problems and deal with it. I’m certainly strong enough and I’ve been here before. I know how it works.”

How it works is that Pardew is now the odds-on favourite to be the next manager sacked and is under intense pressure from outside, never mind inside, the club. “That comes with the territory,” he said. “The goals that we conceded today don’t reflect well on us. I’ll do what I always do – reflect on this game and try and correct it for the next one. But six defeats, and a couple of defeats we shouldn’t have had – Burnley and this one – that’s what’s put us in this mess that we’re in.

Facebook Twitter Pinterest A dejected looking Alan Pardew. Photograph: Christopher Lee/Getty Images

“The last 20 minutes was as crazy as I have ever seen. If we can’t defend at 4-3 with about six minutes on the clock, I’m afraid that’s not good enough. We just can’t seem to defend set-plays; that’s four today. All four of them I think we should do a whole lot better than we do. I’m going to have a look at that and possibly make changes.”

With Pardew’s position under so much scrutiny and Palace in freefall, it was easy to overlook just what this result means to Swansea. It was their first victory since the opening day of the season and while their defending was every bit as calamitous as Palace’s at times the result was everything for Bob Bradley and his players, who showed tremendous courage to claw their way back into a game that looked to be beyond them.

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Gylfi Sigurdsson was outstanding, Leroy Fer scored twice and Llorente showed the sort of predatory touch in front of goal that has been so badly lacking up. At the other end of the pitch, however, Swansea were an accident waiting to happen, with Wilfried Zaha’s opening goal exposing familiar failings as the winger wriggled clear of Neil Taylor before drilling home.

Sigurdsson then equalised with an exquisite free-kick and Palace started to lose their way, not helped by a potentially serious injury to Connor Wickham, who left the field on a stretcher. Fer struck twice in two minutes, stabbing home after Llorente’s header was cleared off the line and turning in again from close range after a Sigurdsson free-kick. Then came the Palace comeback.

James Tomkins reduced the deficit from inside the six-yard box, Jack Cork headed Zaha’s cross into his own net in farcical circumstances and Benteke hooked home off the post after Scott Dann had won yet another header in the Swansea penalty area. Swansea looked finished, yet they were anything but as Llorente scored twice from close range, to delight of their manager.

“It’s a turning point in many ways,” said Bradley, who now has his first win in six matches. “At the most difficult moment the players showed character and that’s going to pay off for them. Today has got to be something that we enjoy.”