Despite the defeats, MPs will debate the customs union and single market again in the coming weeks, when pro-European Conservatives are seeking to amend two other bills. She now relies on the support of a small Northern Irish party.
In parliament, May told lawmakers she had agreed with Brexit minister David Davis to "bring forward an amendment in the (House of) Lords".
British Prime Minister Theresa May looks set to avoid an embarrassing defeat in parliament on Wednesday over her post-Brexit trade plans, a day after she defused a rebellion in her party over plans to leave the European Union.
Facing the prospect of losing a vote on a crucial amendment to the government's flagship Brexit legislation - which was created to empower parliament to vote down the final deal without risking a "no-deal" exit from the bloc - ministers intervened with a concession at the 11th hour even as MPs were wrapping up debate on the controversial measure.
The deal to avert the rebellion, thrashed out on the benches of the House of Commons just minutes before voting, was for the government to discuss changes to the bill which would hand lawmakers more control over the Brexit process.
Before leaving for Canada, May was forced into crisis talks with her Brexit minister who had challenged her so-called backstop plan to ensure no hard border on the island of Ireland.
Yet over the course of a few days, the Prime Minister has, apparently, turned things around. Many felt this was nowhere near enough time to really get to grips with so many points - especially given the importance of numerous amendments.
Marcus Rashford picks up 'knock' in England training Harry Kane insists that the World Cup remains the pinnacle of football, despite club competitions increasing in prominence. Constantly trying to improve, playing in a style that we've used in the past year or so and that people have warmed to.
The government won the EEA vote comfortably after Labour abstained, although a handful of Tory MPs, including former attorney general Dominic Grieve, indicated they would back the motion. Amber Rudd, the ex-Home Secretary and a leading supporter of Britain remaining in the European Union, and Iain Duncan Smith, a prominent campaigner for Leave, co-wrote an article urging unity among Conservatives.
He joined four other Labour MPs who quit the party's frontbench to back an amendment from the House of Lords that would keep the United Kingdom in the EEA.
By a vote of 324 to 298, the House of Commons on Tuesday rejected a move to give lawmakers the power to send the government back to the negotiating table if they don't like the terms of the Brexit deal struck with the EU.
It seems that May will survive as Prime Minister - for now at least.
The BBC's political editor Laura Kuenssbergsaid she had been told by a government source that no actual concessions had been agreed and the only agreement was to keep talking. Yet how long will this unity last?
Ukip leader Gerard Batten said: "The only "meaningful vote" was the verdict of the people in referendum of June 23 2016".
Tory MP and former education secretary Justine Greening, who supported Remain in the European Union referendum, told Sky News in response: "I think what we all need to recognise is that the positions people are taking on Brexit are genuine and passionately held - and should be respected".
It warned the idea would lead to a hard border between Northern Ireland and the Republic because it does not cover regulatory checks.