A stunning goal from Jay Rodriguez four minutes from time raised the temperature at a frozen Turf Moor as the Clarets left it late to avoid a sixth home defeat of the season.
The Clarets' top-six hopes were put on ice, for the time being at least, as they struggled to cancel out Paul Taylor's early goal in blizzard-like conditions.
But a storming second-half fightback finally brought them some reward thanks to that man Rodriguez.
The striker is in the form of his life and after striking twice in mid-week to fell Forest, did it again to move to 17 for the season.
This time the former England under-21 international did almost all the hard work himself to produce a magnificent solo effort and make it five goals in five games.
And while the Clarets ultimately paid the price for a sloppy start, their determination not to finish empty-handed at least earned them a point towards what could still be a play-off total in three months' time.
Touch of class as Jay-Rod makes it 1-1
After scoring early in winning at Nottingham Forest in mid-week to put the play-off places within touching distance, the Clarets almost did it again through Charlie Austin, who scuffed a shot wide at the second attempt after a long throw-in from Ben Mee had dropped for him eight yards out.
But that's where the similarities ended in a first half which was as poor as anything Burnley had produced since launching their winning streak back in November.
Peterborough had been one of the teams to capitalise on the Clarets' early season uncertainty with a 2-1 win at London Road and they belied their recent poor form with an impressive display that could have yielded more than a one-goal lead by the break.
Burnley's defence looked nothing like the rock-solid unit that had kept six clean sheets in their previous seven games as they were undone after 12 minutes.
Austin had just headed at Joe Lewis at the other end when a long clearance from the Posh keeper was flicked on for Taylor to pounce on hesitation from Ben Mee and rifle a shot past Lee Grant.
Paul Taylor puts Posh in front
That was far from a flash in the pan as Peterborough cut through almost at will and when David Edgar and Michael Duff got in each other's way, David Ball skipped through to hit a low shot against the inside of a post.
The lively George Boyd also flashed an effort wide when he should have done better after Tommy Rowe had weaved his way into the penalty area.
And in freezing conditions, Burnley's response was invariably laboured. Ross Wallace saw a shot rear up awkwardly for Lewis and bounce off the keeper who was doubtless relieved to see Mee direct a shot just wide as he looked to make amends for his earlier mistake.
But the keeper's only real save of the half was a close-range parry to keep out an Austin header as Burnley at last strung together a few passes and gave Kieran Trippier the chance to deliver a typically inviting cross.
Charlie Austin goes close in the first half
And the improvement continued after the break as the Clarets, now playing in a snow storm, wound it up in search of an equaliser.
Rodriguez was invariably the main threat as he worked space around the edge of the penalty area for a couple of goal-bound efforts, although it was set-pieces that remained the most likely source of a goal.
Josh McQuoid failed to connect cleanly from a Wallace free-kick and then when Trippier swung over another one Chris McCann headed over from in front of goal.
The Clarets' tried and tested corner routine almost let in Rodriguez after his inital shot had been deflected wide and with 20 minutes to go Burnley were virtually camped around the Peterborough penalty area as the blizzard finally abated.
Eddie Howe sent on Keith Treacy to try and save the day and the winger quickly got behind the visitors' defence to pull another ball across the face of goal.
Amid growing frustration the visitors looked to have weathered the storm and got a slice of luck with five minutes to go when full-back Mark Little looked to block a Wallace shot with his raised hands.
Chris McCann drives the Clarets forward
But the Clarets kept going and after McCann had shot over and Austin had forced Lewis to save, Rodriguez produced his piece of magic to make it 1-1.
Picking the ball up just inside the Posh half the striker was surrounded by black shirts.
But in his current form there is no stopping him and Rodriguez duly waltzed his way through before calmly steering the ball past Lewis and into the corner of the net to give the Clarets the least they deserved.
Burnley: Grant, Trippier, Mee (Bartley 75), Duff, Edgar, Marney (Hines 83), McCann, Wallace, Rodriguez, Austin, McQuoid (Treacy 70). Subs: Easton, Jensen.
Peterborough: Lewis, Little, Bennett, Zakuani, Alcock, Boyd, McCann, Rowe, Frecklington (Tunnicliffe 70), Ball (Tomlin 75), Taylor. Subs:Sinclair, Kearns, Jones.
Referee: Colin Webster.