Labour's shadow Brexit secretary Sir Keir Starmer described the result as "disappointing", accusing the PM of "buying off her own MPs at the eleventh hour".
After pro-EU Conservative lawmaker Dominic Grieve said he would support the government's proposal for a "meaningful vote" in parliament on any Brexit deal, a potential rebellion that could have undermined May's authority looked was averted.
The European Parliament's chief Brexit negotiator wants the United Kingdom to have an "association agreement" with the EU.
May has offered parliament a vote on the final terms of Britain's withdrawal from the European Union, but has been engaged in months of negotiations over what happens if it is rejected.
The government was anxious enough about losing today to budge, even if they only gave an inch.
Francis Elliot, the political editor of The Times, reported seeing a sick MP being helped out of a vehicle and into the Houses of Parliament in order to take part in the vote.
"Whichever way the vote ultimately goes, the idea that the Government is going to be endangered by this difference of view within the House of Commons which might lead to its defeat is complete nonsense".
FPJ's dream XI predictions for Serbia and Switzerland; Live Blog
Switzerland boss Vladimir Petkovic has refused to ignite a political row ahead of their key World Cup clash with. The two Swiss internationals, of Albanian origin, turned the game around with strikes they will never forget.
MPs in the House of Commons voted to reject a motion that would have strengthened the power of lawmakers to intervene if no deal is reached with Brussels before Brexit in March 2019.
Six Tory MPs - Ken Clarke, Anna Soubry, Sarah Wollaston, Heidi Allen, Antoinette Sandbach and Phillip Lee - rebelled while four Labour MPs backed the government and six other Labour MPs abstained, as did Kelvin Hopkins, who sits as an independent after having the whip withdrawn.
In a sign of how close Wednesday's vote was, heavily pregnant and sick MPs were called in to cast their ballots, including one in a wheelchair. He also said he had been reassured by a statement saying it was up to the parliamentary speaker to grant lawmakers greater influence over ministers.
Britain's upper house of parliament will consider any changes made to proposed Brexit laws on Wednesday evening, shortly after they have been voted upon by the lower house of parliament, the opposition Labour Party said.
The Brexit Withdrawal bill will now go back to the House of Lords where it is nearly certain to be supported, paving the way for Royal Assent by Queen Elizabeth II.
Mr Grieve said he had insisted on a key paragraph in the government statement accepting "it is open to MPs to table motions and debate matters of concern and that, as is the convention, parliamentary time will be provided for this".
Nicky Morgan, another frequent rebel who backed down yesterday, echoed Grieve's sentiments that she did not wish to see May "destabilised or undermined" ahead of next week's summit of European Union leaders, but warned of further battles to come over the UK's trade and customs arrangements with the EU.