Aaron Mclean scrambled home a stoppage-time equaliser to earn Peterborough a vital point in a dramatic2-2 draw at London Road.
Chris Whelpdale hammered home an opener for the home side after Swansea had dominated the first half but Swans substitute Lee Trundle scored twice in the final six minutes to put Paulo Sousa's men on the verge of victory.
But Mclean converted with the last chance of the match to give Mark Cooper's side a share of the spoils.
Posh had looked set for a much-needed win before Trundle's intervention but now remain rooted to the foot of the table and need wins soon if their stay in the second tier is not to be a short one.
The Swans kicked off on the fringe of the play-off places and dominated the first-half with their eye-catching possession football.
Winger Thomas Butler shot straight at Peterborough goalkeeper Joe Lewis in the second minute before Andrea Orlandi twice came close to finding an opener for the visitors.
A bright passing move ended when Orlandi drove in low from the edge of the area and, despite the ball taking a deflection off Exodus Geohaghon, Lewis recovered well to make a sprawling stop.
Orlandi then saw another deflected shot fly just wide of the far post as Cooper's men struggled to get hold of the play.
Angel Rangel delivered a magnificent cross from the right as the half drew to a close but both Darren Pratley and Jordi Lopez failed to get on the end of it.
Posh started the second period in more competitive fashion and their first effort on target in the 51st minute.
Whelpdale whipped in a cross from the right and midfielder Lee Frecklington got ahead of his marker to angle a header in on goal from the centre of the penalty area but Dorus De Vries was alert to make the save.
Cooper's side were on song and went ahead in the 55th minute.
Geohaghon launched a trademark huge throw into the heart of the penalty area, and after Federico Bessone failed to hook the ball clear, Whelpdale steadied himself to thump a drive past De Vries and into the roof of the net.
Whelpdale then forced a fine save from De Vries with a thunderous low shot after Craig Mackail-Smith's clever back-heel, before Mackail-Smith should have doubled the lead.
A pass forward caught out the Swansea backline and Mackail-Smith was clean through, but hesitated and could only shoot at De Vries' legs.
Sousa introduced Trundle from the bench and the talismanic striker grabbed the leveller with six minutes left.
Gorka Pintado found the forward with his back to goal and after he managed to hold off a challenge Trundle angled in a low shot past Lewis.
The drama was not over and Trundle added a copybook second in the final minute.
A long ball forward was chased down by Trundle and he again proved too strong for the defence and, after wriggling clear, shot past Lewis at his near post.
That looked to have snatched a win for Swansea but Mclean found time to level.
Captain George Boyd skipped away down the left and drove in a low cross which was missed by two defenders to allow Mclean to steer home at the far post.
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