The pro-European cause was boosted when junior justice minister Phillip Lee, a close personal friend of the prime minister, resigned shortly before the debate in order to back the veto amendment.
The Government has managed to fend off a major rebellion after parliament rejected an amendment to bring a "meaningful vote" on the final Brexit deal. It also increases the prospect of MPs forcing a referendum on the terms of the eventual deal or even of a snap election before the end of the year.
Theresa May met with rebel backbenchers moments before MPs voted on an amendment to the EU Withdrawal Bill which would have given them the power to tell her to go back and renegotiate the Brexit deal.
Senior Remainer Dominic Grieve said Mrs May promised to table amendments in the House of Lords which will address their concerns.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union. "And I can not bring myself to vote for it in the bastion of liberty, freedom and human rights that is our Parliament".
Dr Lee added: "If Brexit is worth doing, then it is certainly worth doing well; regardless of how long that takes".
Lee said "the people, economy and culture of my constituency will be affected negatively" by Britain's European Union departure, and it is "irresponsible to proceed as we are". "Labour will only vote for a final Brexit deal if it delivers a strong relationship with the single market based on full tariff-free access and ensures no loss of rights and standards", Labour leader Jeremy Corbyn said on Facebook.
"The Government's amendment today provides for a meaningful vote".
"I expect the government to honour its commitments and I expect the PM to honour her commitments and I have no reason to distrust the approach she took with us", Mr Grieve told the BBC's Newsnight.
But while the well-worn arguments focusing on the nature of a meaningful vote were made, the real drama was taking place on the floor of the chamber where chief whip Julian Smith, solicitor general Robert Buckland and Brexit secretary David Davis as well as the Prime Minister's parliamentary private secretary (PPS) George Holingberry were in deep discussion with each other and Grieve, as they sought to avert an embarrassment for the government.
Despite many Conservative MPs who backed Remain in the referendum, just two rebelled against the government on a meaningful vote. "We have no doubt of what was going on".
However, Devon Tory Sarah Wollaston signalled that she would back Mr Grieve's amendment.
As the clock ticked down to the vote, two rebels stood up to say they were satisfied with what the government had offered them.
"Grieve's amendment puts that right and in a way Govt could and should accept it".
A spokesperson for the Department for Exiting the European Union said: "On the meaningful vote we have agreed to look for a compromise when this goes back to the Lords".
Government sources signalled to the Press Association that ministers were set to back the move.