They subsequently warned they will not be easily bought off, while Tory Brexiteers urged ministers not to concede any ground.
At times ministers engaged in public negotiations from the despatch box, with leading Conservative rebel Dominic Grieve and other rebels later leaving the chamber with the whips to discuss the concessions.
Pro-Brexit members of the government want to be able to play the "no deal" card, but the House of Commons, where pro-EU voices are stronger, would nearly certainly reject the idea.
The battle now moves to the House of Lords, where the government will formally reveal how much it has conceded in the wording of a new amendment expected on Monday or Tuesday.
Mr Grieve withdrew his own amendment, which would have given MPs powers to dictate what the Government should do if no acceptable agreement is reached by February 2019.
"We have not, and will not, agree to the House of Commons binding the government's hands in the negotiations". "I'm fairly confident we will be able to do that".
"The House is made up of 651 robust individuals whose position gives them a powerful say in what the executive can and cannot do".
"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".More news: World Cup organisers make final touches to Luzhniki Stadium
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In his resignation letter, he said he wouldn't be able to "look my children in the eye" if he supported Brexit in its "irresponsible" current form.
The government won the first set of votes Tuesday, but looked set to face defeat on the issue of whether Parliament should have a "meaningful vote" on the Brexit deal.
'(It's) too soon to make a decision on that, but we'll have to consider it in the months ahead'.
Fellow Tory Remainers Anna Soubry and Ken Clarke were not convinced by ministers' concession and voted against the government by backing the Lords amendment on a "meaningful vote".
She also explained she was exhausted of MPs approaching her in "quiet and dark corridors", of British businesses who demand private meetings where they "lay bare their despair but refuse to go public", and those commentators who encourage her to keep going in the face of death threats.
Soubry reminded the House of Commons of the 48% who were being ignored by the government.
Asked whether such concessions would nowAsked whether such concessions would hamper Britain's negotiating hand, Mr Grieve continued: "I disagree with that entirely".
In the event, Dr Lee abstained on the crucial vote, saying he was "delighted" the Government had agreed to introduce an amendment giving Parliament "the voice I always wanted it to have in the Brexit process". He said: "Facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".