Goals at either end of a fluctuating contest from Charlie Austin and Martin Paterson were not enough for the Clarets to bury their Peterborough hoodoo but did at least bring them a rare reward at London Road.
Fit-again striker Austin marked his return from injury with a first-minute goal as he took his tally for the season to 24.
But after a quick-fire second-half blast from Peterborough defender Tommy Rowe, it took an 85th-minute equaliser from substitute Paterson to spare the Clarets defeat to the Championship strugglers.
Burnley have only ever won once in ten attempts at Peterborough and have lost in four of their last five visits.
And when Rowe capped a second-half fightback from the Posh it looked like history would repeat itself.
But Sean Dyche’s men are nothing if not fighters these days and with their play-off hopes facing the prospect of another setback with a second successive defeat, they staged a comeback of their own to earn a share of the points thanks to Paterson’s late intervention.
Having been forced to sit out all of January, it took Austin just 60 seconds to announce his return as he fired the Clarets in front from his first sight at goal.
Ross Wallace’s floated ball into the penalty area was perfectly placed but it still took the predatory instincts of Austin to make it look a routine finish as he stuck out a leg to steer a volley beyond Bobby Olejnik from ten yards out.
It was the perfect start for the Clarets and gave them the platform to play the first half largely on their terms and not look to force the issue.
That was never likely to be easy on a poor playing surface that made passing and dribbling with the ball a hazardous business.
Twice Danny Ings should have made more of driving runs into the penalty area and Junior Stanislas also threatened without delivering a killer punch when a second goal would have made it an uphill fight for the bottom club.
But Peterborough did enough before the break to suggest that theirs was not a lost cause with George Boyd and Lee Tomlin causing problems.
Boyd’s vision looked far from impaired as he played his usual creative role, despite failing a medical at Nottingham Forest less than 48 hours earlier for supposedly defective eyesight.
And Tomlin belied his less than streamlined appearance with some tricky footwork and elusive running that periodically had Burnley on the back foot.
But with Michael Duff - also back in business following a hamstring injury - and Jason Shackell reunited in the centre of the Clarets’ defence and proving determined not to pass, goalkeeper Lee Grant spent the first half as a spectator without a shot to save.
That situation changed almost immediately at the start of the second half as Grant was forced to drop onto a shot from Dwight Gayle after the skilful Tomlin had chipped a more threatening effort just wide.
And ten minutes in the battle lines were re-drawn as the Clarets lost Duff to a calf injury and the Posh threw on wingers Nathaniel Mendez-Laing and Tottenham loanee Alex Pritchard.
With Dwight Gayle also coming alive, testing Grant again and then shooting just wide, it began to look as though one goal might not be enough and the Clarets had chances to give themselves breathing space.
Stanislas curled an effort wide when well placed and Ings then combined well with Stanislas and Austin to work a shooting chance which might have demanded a more difficult save from Bobby Olejnik.
And with Burnley failing to kill the hosts off, they were rocked by two goals in five minutes as Peterborough’s adventure was rewarded.
The first, hooked in by Rowe, came after the Clarets couldn’t clear a corner and the ball bounced around the penalty area for the captain to pounce.
And then when Dyche’s men were again caught at full stretch on the break, Rowe strode forward from left-back to make the most of a fortunate ricochet on the edge of the penalty area to hammer a shot past Grant.
Suddenly the onus was on Burnley to try and mount a response and after getting over the shock of surrendering their lead they mounted a successful late fightback.
Dyche had sent on Sam Vokes and Paterson to offer some fresh legs and an extra forward presence and the move paid off with just five minutes to go.
The Clarets had been turning up the heat when Danny Lafferty and Chris McCann forced the decisive opening down their left flank.
With Lafferty releasing McCann, the midfielder weaved his way into the box and squared the ball perfectly for Paterson to side-foot home from just a couple of yards out.
It was Paterson’s first goal since the start of November but in stoppage time he almost added another as Burnley were only denied a winner by the brilliance of Olejnik.
The striker’s back-header from a Stanislas free-kick looked good enough to bag the points but Olejnik reacted superbly to tip the ball over the top for a corner and deny Burnley a dramatic victory.
Burnley: Grant, Trippier, Lafferty, Duff (Edgar 54), Shackell, Marney, McCann, Wallace (Vokes 68), Austin (Paterson 74), Ings, Stanislas. Subs: O’Neill, Stock, Treacy, Jensen.
Booked: Trippier 34, Shackell 43
Peterborough: Olejnik, Bostwick, Zakuani, Knight-Percival (Prtichard 55), Little, Boyd, McCann, Newell (Mendez-Laing 55), Rowe, Tomlin (Payne 85),
Gayle. Subs: Brisley, Petrucci, Gordon, Day.
Referee: Andy D’Urso
Attendance: 6,648 (Burnley 956)