MPs voted 324 to 298 to reject the proposal, which had come to parliament after the Lords brought amendments to the EU (Withdrawal) Bill.
The issue seen as most likely to provoke a rebellion was that of giving MPs a "meaningful vote" on the final Brexit deal.
Our lobby team has also been told by Conservative sources that four more junior ministers were considering following Lee by quitting their jobs as part of a coordinated plot to scupper May's Brexit plans.
"The Government's amendment today provides for a meaningful vote". That effectively rules out threatening the European Union with a no-deal Brexit, because the Commons will not approve a no-deal Brexit.
This led him not to force his own amendment to a vote, while the potential rebels backed away from voting against the government on a similar House of Lords amendment, thereby allowing ministers to remove the peers' changes to the bill. "It was the prime minister who I sat in front of this afternoon and who gave us those assurances".
They did so by offering a concession to Tory backbenchers.
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".
"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".
Conservative lawmaker Phillip Lee, who voted to remain in the European Union in Britain's 2016 referendum, resigned as a justice minister so he could vote against the government on a key measure.
"The main reason for my taking this decision now is the Brexit process and the government's wish to limit parliament's role in contributing to the final outcome in a vote that takes place today", Lee, who voted to remain in the European Union during Britain's 2016 referendum, said on his website.
"This justifies my decision to resign and makes it a lot less painful".
Due to the concessions offered, the details of which have not yet been fully revealed, two Conservative MPs - Ken Clarke and Anna Soubry - rebelled.
MPs were told that one parliamentarian had to be accompanied to a public meeting by a six armed police officers because of threats over their stance on Brexit.
May's decision to leave the customs union, which sets tariffs for goods imported into the EU, has also been criticised for raising the prospect of a "hard" border on the island of Ireland, which some fear could reignite sectarian violence.
Brexit minister David Davis had earlier warned lawmakers that the government would never allow them to "reverse Brexit" or undermine negotiations. One says: "If we do not get what we were promised the Government will be defeated after we have amended the Bill in the Lords".
Meanwhile, Tory Brexiteer Bernard Jenkin told the government he would not accept ministers agreeing to Mr Grieve's demand for the House of Commons to assume control of Brexit negotiations in the event of no deal.
Theresa May ultimately persuaded all but two of her MPs to back her in the decisive vote in Westminster on Tuesday - but she increasingly appears little more than a hostage to the warring factions in a bitterly divided Conservative party.
British Prime Minister Theresa May narrowly avoided a major blow to her Brexit strategy Tuesday after MPs rejected a plan that would have given parliament a veto on the final deal negotiated with Brussels.