Jay Rodriguez's solo goal rescued a point for Burnley and denied Peterborough their first Championship win since Boxing Day.
The 22-year-old striker slotted home three minutes from the end after a mazy run past four Posh defenders.
Paul Taylor had put the visitors ahead after a mistake from Ben Mee, before David Ball came close to a second.
Chris McCann headed over for the Clarets, who also had a penalty appeal turned down, before Rodriguez's strike.
The draw leaves Burnley just two points, but five places, off the play-off places while Peterborough have taken only two points taken from five league games in 2012.
Taylor smashed past goalkeeper Lee Grant after Mee's slip had let him in and Peterborough were within a post's width of doubling their lead when Ball's shot rebounded off the woodwork.
Charlie Austin drew a great save from Joe Lewis at the other end in a rare first-half chance for the hosts before seeing an effort cleared off the line from a Josh McQuoid cross after the break.
Referee Colin Webster waved away the home side's appeals for a penalty when Ross Wallace's shot hit defender Mark Little, but Rodriguez had the last say with a special goal.