In the preceding vote, the government had fallen to only its second defeat on Brexit in the Commons, as MPs voted by 305 to 301 for continued United Kingdom involvement in the EU's regulatory system for medicines.
Mrs May's majority was cut to just three votes after she adopted Brexiter amendments to a key piece of customs legislation, and the proposals narrowly passed through the House of Commons late on Monday.
Twelve Conservative MPs rebelled against the government to vote for a proposal that would have kept the United Kingdom in the customs union if no alternative plan for frictionless trade with the EU had been agreed by January 2019.
Highlighting the fine margins May is dealing with, Tuesday's victory required the votes of four pro-Brexit Labour opposition lawmakers who backed the government in defiance of their party's instructions.
This article has been adapted from its original source.
In dramatic scenes in the House of Commons, ministers...
"Barnier can bluster, Vardkar and Coveney can foot stamp all they like, but the fact remains that the prime minister has now got the support of whole of parliament in opposing their demands that Northern Ireland would stay in the single market and customs union", he said.
She will also address a group of her backbench MPs this evening.
May denied a suggestion in parliament that her Brexit plan was dead, and her spokesman said the decision to accept those amendments were "consistent" with the white paper policy document ministers agreed earlier this month.
Pakistan readies for disgraced ex-PM Sharif's return from UK
The former prime minister and his daughter were in London, where Sharif's wife Begum Kulsoom is undergoing treatment for cancer. Sharif, who was disqualified by the Supreme Court past year in the Panama Papers case, is now the supremo of the PML-N.
Mr Hollingbery, moving the Government's amendments to the Bill, said: "I recognise that members are seeking reassurance that the government will be transparent about the content of these transitioned agreements and what might need to change to deliver this continuity that we have championed for so long".
The government said being part of an EU customs union would prevent it from striking worldwide trade deals, won the vote by 307 to 301, a slim majority for May of just 6.
Britain's European Union membership was critical to United States interests, with the policy underpinning the agenda of all UK governments since Britain entered the European Union in 1975.
"Theresa May is in a more hard position than I was", he told ITV News.
The idea of a referendum sequel has always been popular among Remainers - those who voted to stay in the European Union - who believe that the campaign around Brexit was infused with lies and propaganda, and that Leavers, their opponents, never had a coherent plan for withdrawal.
But Mrs May suffered a setback when another rebel amendment, seeking to keep the United Kingdom in the European Medicines Agency, was passed by the Commons. Eight officials have quit since that summit, including two very high-profile Leave advocates, David Davis and Boris Johnson.
The Prime Minister then heads for her most challenging date of the day, where she will appear before the 1922 Committee of backbench Tory MPs.
On Monday (16 July), the other wing of May's Conservative Party - those MPs who want to keep the closest possible ties with the European Union after Brexit - spoke up in the voice of former education minister Justine Greening who called for a second referendum.