The decision was taken during the opening stages of the debate on the Queen's Speech programme for the last, pre-election session of Parliament; a package stripped of all but the bare essentials.
After Tony Blair had repeated Labour's offer of full support for the two uncontentious bills, the Prime Minister held hurried consultations with Cabinet colleagues on the Government front bench.
Then, replying to the Labour leader's attack on the Queen's Speech, Mr Major staggered MPs in all parts of the House by accepting Mr Blair's offer. "I accept that," he said. "I accept that deal."
For more than 24 hours, ministers had insisted that the creation of a paedophile register - promised by Michael Howard, Home Secretary, in a speech to this month's Conservative Party conference - and the long-awaited bill on stalking, would have to be carried through the Commons by backbench MPs using the high-risk Private Member's Bill procedure.
But, having been ridiculed for an abdication of responsibility by some politicians and The Independent, the Prime Minister was clearly itching for an escape route, which he seized on when Mr Blair renewed his standing offer.
Mr Blair immediately intervened to say he was "delighted" by the remarkable concession. "It shows the country what we can achieve in opposition," he said. Paddy Ashdown, Liberal Democrat leader, told the House that it was the "fastest U-turn in political history".
Certainly, it ranks as the most brazen and snappy U-turn of a Government responsible for the withdrawal of sterling from the European exchange rate mechanism, the dropping of EU non-cooperation over the beef ban, and the decision to stage a referendum on entry into a European single currency.
But that did not stop the Prime Minister's office and senior ministers denying any change of tack. Michael Forsyth, Secretary of State for Scotland, told BBC Radio: "I don't know how you can describe this as a U-turn. It is a U-turn on the part of the Opposition to say that they are not going to oppose Government measures concerned with crime."
Hoping for a hat-trick, the shadow Home Secretary, Jack Straw, said last night that Labour was also offering full support for legislation against sex tourism, another of Mr Howard's party conference promises jettisoned from the Queen's Speech.
Mr Major told the Commons that there had never been any question of putting the paedophile and stalking bills in the Queen's Speech, though that was not the impression given to Tory representatives in Bournemouth.
As for the decision to use the Private Member's Bill procedure, that was being stoutly defended by senior ministers at lunchtime yesterday, with Stephen Dorrell, Secretary of State for Health, telling BBC Radio: "It is an absurd proposition to say that we should not use the uncontroversial bills procedure designed for private members - not to use that to put through uncontroversial bills."
But the point made all along by Labour and the Liberal Democrats was that if the Bills were so uncontroversial, nothing could be quicker than government legislation carried through in Government time.
Donald Dewar, Labour chief whip, said last night: "It is clear that the Prime Minister changed his mind literally mid-speech, forced to give ground and seeing an opportunity for scuttling. It shows a good deal of confusion at the heart of Government."
Mr Major, however, drew the line on a further retreat; standing firm against Mr Blair's call for a free, unwhipped vote on calls for a total ban on all handguns. Given the decision by the Liberal Democrats to support a total ban, and with some Tories ready to rebel on the issue, the Government faces the real risk of defeat, unless it performs yet another U-turn, closer to the vote.
With the Government facing an election deadline of next May, the Queen's Speech, which identified 13 bills for action on key political battlegrounds such as education, health and law and order, was one of the shortest for years.
While Mr Major cautiously made no mention of Europe in his speech to the House, he did go out of his way to stake out the ground on the Ulster peace process, with a tough warning to Sinn Fein and the IRA.
He warned that Sinn Fein could only join all-party talks if "real commitment" was shown to the peace process.
"So even if a new ceasefire is declared," he told the House, "there will have to be more than soft words to convince the Government ... that it does not represent another tactical device to be abandoned at any convenient moment."
The stalking bill
Stalkers could face up to five years in jail and an unlimited fine by next year under the deal accepted by John Major yesterday.
Anyone using words or behaviour on more than one occasion - twice would be enough - which puts their victim in fear of violence will be at risk of the penalty. A lesser offence, designed to catch words or behaviour causing harassment, alarm or distress, would carry up to six months' imprisonment and/or a pounds 5,000 fine.
In a significant improvement on current criminal law, victims will not have to prove actual intent, and the new laws are designed to cover a range of activities from unwanted gifts and telephone calls to physical threats. Courts would also have the power to make a restraining order immediately after convicting a stalker of either of the two criminal offences. Breach of either of these civil orders would be a criminal offence.
The sex offenders bill
The promised Government measure to clamp down on paedophiles and other sex offenders may be one of the quickest political climbdowns in recent political history, but the bill that is now set to emerge is likely to be limited.
The measure would create a national register of convicted paedophiles and other sexual offenders. But most of the other proposals in a June White Paper have been put on ice. The suggestion that sex offenders be subject to extended supervision on release from prison forms part of the Crime (Sentencing) Bill, but three further proposals are on the back-burner. These were that it should be a criminal offence for convicted sex offenders to seek work involving children, that DNA testing be extended to include 3,500 sex offenders convicted prior to new powers in the 1994 Criminal Justice and Public Order Act coming into force, and supervision of defendants' access to victim statements and photographs.