The House of Commons voted 324 to 298 to defeat an amendment to the EU (Withdrawal) Bill which would have removed her government's power to decide to leave the bloc without any agreement.
Before the vote, she assured lawmakers she would honor her promise and deal with the "concerns raised about the role of parliament in relation to the Brexit process".
Pro-EU Conservatives have signalled they remain ready to rebel on Theresa May's flagship Brexit Bill if she fails to deliver a truly meaningful vote for MPs on the divorce settlement.
Former Tory cabinet minister Dominic Grieve, who tried to broker a compromise between MPs and ministers, has warned a no-deal scenario could lead to a "national crisis".
May objected to the amendment - inserted by the House of Lords - because she said it would tie her hands in the negotiation. Yet another Brexit contradiction it seems and one that rebel, and opposition MPs need to keep a close eye on. As ever, Delano will keep you posted.
Speaking to City leaders, John McDonnell said: "We campaigned for Remain but many of our MPs, including myself, now represent seats which voted heavily Leave".
The Labour Party's Chuka Umunna, who backed staying in the European Union, welcomed the concession as the end of the government threatening to allow Britain to crash out of the European Union without a deal. But a government official said they had just agreed to open talks on the basis of the rebel amendment.
Earlier on Tuesday the government suffered a setback as one minister resigned over what he called the government's plans to "limit" the role of parliament in shaping Brexit. Known as ping-pong, the bill will move between the commons and the lords until both sides are in agreement on the text - or until the government has made enough concessions for the lords to back down.
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Blogger Sandra Rose noted: "This is a flawless example of narcissistic celebrities who will do and say anything to stay relevant". During the latest episode of Jada Pinkett Smith's Facebook Watch show Red Table Talk , the topic was all about sex and pleasure.
Labour MPs had been whipped to abstain on the motion to disagree with the Lords EEA amendment.
Mr Grieve said no government would survive if it tried to dispense with Parliament's input.
Labour opposed the EEA model and introduced its own amendment, tabled by Sir Keir Starmer, which was defeated by 82 votes on Wednesday night. The government wants the Commons to reject 14 out of 15 amendments introduced by the Lords which are meant to keep Britain close to the European Union after Brexit.
The government won all 11 votes in the House of Commons yesterday, on topics including the use of "Henry VIII" powers to make changes to domestic legislation after the United Kingdom leaves the European Union by way of regulations and one whether the date of departure should be given statutory effect.
In such an event, he said Parliament should be able to flex its muscles by requiring ministers to come forward with a plan of action, which MPs would be able to debate and vote on. Brexit supporters will be watching closely to see what concessions the government finally offers to the rebels.
May says the changes would weaken the government's negotiating position, and the government will try to alter or reverse them in the House of Commons on Tuesday and Wednesday. "It is the Labour Party that is trying to stop us getting a deal for the British people".
Since there is certainly no majority among MPs for no deal - which all but a hard core of Brexit ultras believe would be disastrous - that now makes no deal extremely unlikely.