Palace won the first corner of the game on five minutes when a Yohan Cabaye cross was blocked and from that set piece, the ball fell to Christian Benteke, after a Scott Dann header had been scrambled clear, but the striker put the chance over the bar.
Just before the quarter hour mark of the game Wayne Hennessey was called into action for the first time as the home side broke but a shot from inside the box by Gylfi Sigurdsson was easily saved by the international goalkeeper.
The visitors got the breakthrough on 19 minutes when Benteke’s flick on was met by Wilfried Zaha and he got the better of his man, with a fine turn, before driving the ball low past Lukasz Fabianski into the back of the net.
Swansea came straight back at Alan Pardew’s side and Hennessey got down to stop a deflected shot by Leroy Fer and then Martin Kelly was on hand to head behind a cross from the left hand side of play.
Just before the half hour mark saw Fabianski have to save low down his right in front of the post to save a header, at the second attempt, from Connor Wickham as he got on the end of a cross from Kelly.
The home side were back on level terms nine minutes to the break as Gylfi Sigurdsson converted a free kick from the edge of the box after Jason Puncheon was penalised for a foul on Jack Cork. A delay in play while the wall was set up was followed by the set piece being placed over the wall and into the net past Hennessey.
Just two minutes later and Palace nearly regained the lead as Cabaye went round the ‘keeper and then his cross finds Zaha, whose effort hits the bar and the rebound falls just out of reach of both Benteke and Wickham.
Swansea ended the half with a couple of chances on goal, former Eagle Wayne Routledge saw a shot go over the bar and then two minutes before the break, Modou Barrow, in the box, fired over the bar when well placed in front of goal.
The sides went into the break on level terms as that free kick cancelled out the opener from Zaha on 19 minutes.
The start of the second half was marred by an injury to Wickham, as he made a challenge he went down and had to bestretchered off on 51 minutes, to be replaced by Andros Townsend.
A couple of early corners in the half to Swansea after some good defending cleared danger. Kelly got in to block a cross from Barrow and then three minutes later a superb last ditch tackle from James Tomkins denied the same player as he was about to shoot at goal.
Just past the hour mark Routledge got on the hand of a loose ball out of defence but he could only shoot wide of the target as he ran in on goal.
The early second half pressure paid off for Swansea as they came from behind as a corner was headed goalwards by Llorente but his effort was blocked by Cabaye on the line but Fer followed up and gave the home side the advantage.
Three minutes later and Kelly conceded a free kick and the resulting cross from Sigurdsson was met by Fer at the back post and put into the net to extend the lead.
On 73 minutes Benteke won a corner, which was taken by Cabaye and the cross fell to Tomkins and he prodded the ball home past Fabianski to bring the visitors back into the game.
They were not content with that though as a Palace free kick went to Zaha and he played a dangerous ball into the box and and it took a deflection off Cork and went over the goalkeeper into the net and fell into the corner of the net.
Then into the final ten minutes and a corner was put goalwards by Dann and the ball fell to Benteke who, courtesy of the woodwork, snatched a fourth for the visitors as the players and away fans went wild with delight as they came from 2-1 down.
But the Eagles' lead was short-lived. Hennessey did superbly to deny Llorente from point blank range, but the striker got his foot to Sigurdsson's follow up to divert the ball into the net and level the scores again at 4-4.
And there was yet more pain to come for the Eagles as Llorente prodded a loose ball under Hennessey minutes later to give them the lead early into the seven minutes of added time.