The Scottish striker, on loan from Hull, pounced as the game moved into added time to force the ball in from close range after sub David Foley's shot was blocked by the overworked Peterborough defence.
The goal earned that new record, and the clean sheet meant Hartlepool have played 682 minutes without conceding a goal.
Hartlepool dominated most of the game, creating a string of half chances.
Andy Monkhouse sent a long-range shot high and wide of the target, while Duffy headed a Richie Humphreys' left-wing cross wide of the near post.
Peterborough broke out for a chance on 13 minutes, but home keeper Dimi Konstantopoulos saved well after Danny Crow beat the offside trap and cut inside from the left.
Home midfield player Antony Sweeney should have scored on 19 minutes when he swept through the middle and found himself with only Paul Rachubka to beat, but the keeper saved his weak shot with his legs.
The home team were only inches from taking the lead on 38 minutes when Duffy squirmed his way into a shooting position on the left of the area, but his angled shot was deflected wide of the far post by a defender.
Home appeals for a penalty were turned aside three minutes before half-time when Simon Yeo appeared to use his arm to control the ball in his area after a corner.
In the second half, Hartlepool dominated again, but it looked as they weren't going to find a way past keeper Rachubka, who saved well from Duffy and Sweeney, until he was beaten by that late Duffy strike.
The timing was cruel on Peterborough, who had worked their socks off to hold Hartlepool in an effort to bring their run of three consecutive defeats to an end, but they paid for losing concentration late on.