Consequently a defeat on a number of Lords amendments to the European Union withdrawal bill was avoided, but there are further votes tomorrow.
Remain-supporting Conservative MPs had threatened to defeat the government on an amendment to the bill which would have given Parliament a wide-ranging veto to May's Brexit deal, or even force a second referendum.
They subsequently warned they will not be easily bought off, while Tory Brexiteers urged ministers not to concede any ground.
Ministers had initially refused to even consider Grieve's amendment but moved to accept it at least in part, after whips signaled that the government were likely to lose in the Commons.
The debate, which lasted for almost three hours, was split down the usual non-partisan lines that have emerged as a result of Brexit, with the likes of Labour's Kate Hoey and John Mann saying they would back the Conservative government, while Tories including Ken Clarke and Anna Soubry spoke in favour of Grieve.
Leading Conservative rebels welcomed the "important concessions" by the government, but insisted that ministers must follow through on their concession or face a defeat when the bill returns to the House of Commons later this month.
"We had a personal assurance that we would find a way of addressing the concerns which are encapsulated in these amendments", Mr Grieve said as voting continued on Tuesday.
"We will be talking to the government immediately after this in order to find a common way forward. I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible", she said.
"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".
This came after a last-minute resignation by the justice minister Dr Phillip Lee, who said he could no longer look his children in the eye and vote to support the government.
A Lords amendment to the EU Withdrawal Bill would have given MPs the decisive say on what happens over Brexit if they don't agree with the final deal with the EU.
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Neymar is now level with Romario and only behind Ronaldo (62) and Pele (77) in Brazil's all-time record scoring charts. Brazil is in red-hot form after their wins over Germany and Croatia .
"This justifies my decision to resign and makes it a lot less painful".
Well what the Remainer MPs thought they heard from May does not seem compatible with Davis's red lines.
She said unless there was a "meaningful vote" Parliament would be left with "the grim choice between a poor deal and exit with no deal at all".
"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", he said.
As time ticks by, May can no longer kick decisions down the road, increasingly under pressure from European Union negotiators to come up with detailed positions not only on customs, but also on future trade relations and governance.
Asked whether such concessions would nowAsked whether such concessions would hamper Britain's negotiating hand, Mr Grieve continued: "I disagree with that entirely".
However, Devon Tory Sarah Wollaston signalled that she would back Mr Grieve's amendment.
The Prime Minister met pro-EU Tories in her private room in the Commons moments before the crucial vote to hear their demands for a truly meaningful vote on the final deal.
"However, facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".
The new amendment will be written up at a later stage with detailed plans and concessions.
Among the 14 amendments to the Bill - set to be voted on by MPs on Tuesday and Wednesday - are changes which would see the United Kingdom stay in the Single Market and would allow Parliament to dictate future negotiating terms.