The Quakers had fallen behind to James Quinn's first-half strike and only some poor finishing from Peterborough kept the home side in contention.
Indeed, Posh were made to pay for their profligacy in front of goal when Paul Hopkins levelled for Darlington in the 77th minute.
And, just as a share of the spoils looked the most likely outcome, with full-time approaching, Lafferty struck the home winner, volleying under the body of Posh keeper Mark Tyler.
The result was harsh on the visitors, who dominated the first half against a poor Quakers side.
Quinn was guilty of wasting some good chances and Peterborough boss Mark Wright was far from happy after referee Paul Robinson failed to award his side two penalties.
Wright was disappointed that the Hull official didn't spot an infringement when Paul Carden clashed in the box with on-loan keeper Kasper Schmeichel, while he felt Matt Clarke should have been sent off for a foul on Calum Willock in the home box.
"I thought the referee was totally incompetent," fumed Wright. "His handling of the game was okay, but he got the major decisions wrong.
"We should have had two penalties and their lad should have been sent off for the foul on Calum.
"I don't normally criticise refs, but when you don't get those decisions you know things are against you.
"The chances we missed cost us and we really should have been out of sight in the first half.
"The mistake from Mark (Tyler) was uncharacteristic - he has played so well this season."
David Hodgson was in charge of the Quakers side, which lost to Peterborough in the old Third Division play-off final at Wembley in 2000.
But, while this result gained a measure of revenge, Hodgson admitted: "It doesn't make up for 2000, but what it does make up for is the way we improved in the second half after a poor opening 45 minutes.
"We came off at half-time extremely fortunate not to be more than one goal down. But, we stuck at it in the second half and I thought we responded excellently.
"On a scale of one-to-ten I think we were a three in the first half. I knew that once we'd found our feet and started to show some commitment and desire, we would beat Peterborough. That's what we did and we won it.
"I don't want it to become a regular occurrence where we go behind to prove we're good enough to win it.
"We know what we're capable of, but for some reason, we always like to do things the hard way."