Before his about-turn, Grieve had argued that government promises did not hand parliament enough control to prevent the "chaos" that could follow Britain crashing out of the European Union without a deal, and he had seemed to have won over several fellow Conservatives.
Liberal Democrat Jo Swinson came into parliament to vote even though she is several days past the date she was due to give birth.
The rebels sought to amend the flagship bill so they could send the government back to the negotiating table if they don't like the deal, or if talks with the European Union break down.
The government won by a narrow margin as MPs voted 319 to 303 against the amendment that was tabled by leading pro-EU Conservative Dominic Grieve.More news: Merkel, allies avert collision for now in German migrant row
Since a majority of lawmakers favor retaining close ties with the bloc, that would reduce the chances of a "no deal" Brexit, a scenario favored by some euroskeptic members of Prime Minister Theresa May's Conservative minority government.
Some of her opponents on Brexit may simply have chose to keep their powder dry for later fights on issues such as future trading ties with the bloc before Britain's scheduled departure in March next year.
Before the Commons vote, Dominic Grieve, leader of the would-be rebels - who wanted to ensure MPs had the power to stop the United Kingdom leaving without a deal - said the "sovereignty of Parliament" had been acknowledged.
This may be enough to persuade some rebels that their concerns have been addressed, though it is thought likely that ministers will be confident of being able to draft a motion which will be judged neutral by Mr Bercow if the need arises.More news: XXXTentacion dead: How did rapper die? What was cause of death?
Mr Grieve said that the Brexit Secretary's statement amounted to an "obvious acknowledgement of the sovereignty of this place over the executive in black and white language".
"We won't be accepting the Lords amendment", the source said, referring to a decision in the upper house of parliament on Monday to again try to force the government to hand the House of Commons more control over Britain's exit from the EU.
"They have confirmed this could be an amendable motion, with no further constraints on Parliament, giving Parliament a real say on the our country's future".
The government would have been defeated if a rebellion on that scale had materialised.
Lord Hailsham, who led the anti-government rebellion in the Lords described Brexit as a national calamity for Britain, adding that the government's offer failed to deliver a promised meaningful vote.More news: Obama Blasts Trump For 'Ripping Children From Their Parents' Arms'
Not so, insisted ardent Brexiteer Jacob Rees-Mogg, who said all Mr Davis's note did was clarify what the Commons rules were; nothing more.