It was the second setback in as many days for the prime minister, after MPs voted late Tuesday to deny the government certain taxation powers in a no-deal scenario - another attempt to avoid such an outcome.
Brexit-backing Conservative MPs raised numerous "Points of Order", claiming that Mr Bercow had broken Parliamentary rules by allowing the vote, and that he had even ignored advice from his own Clerks in allowing MPs a say on the amendment.
Lawmakers voted 308-297 in favour of demanding the government come up with an alternative plan within three working days after Tuesday's vote, rather than a planned 21-day limit, a largely symbolic vote aimed at putting pressure on the government.
The measure isn't expected to carry significant weight in the event of a no-deal Brexit.
With less than three months before Britain leaves the European Union, there is no indication the country will have any arrangements in place, with the European Union governing issues such as border controls, banking relations and even whether Britons will be able to use their cellphones in Europe.
It is likely to prompt an angry response in Brussels, which has repeatedly rejected efforts to put a time limit on the backstop, meant to avoid a hard border in Ireland if no wider trade deal has been agreed.
Francois read the government's original business motion, which states that additional motions are not allowed.
Mr Grieve had tabled the amendment Tuesday night after pro-EU MPs had passed an amendment to the Finance Bill created to prohibit spending on No Deal preparations without authorisation from Parliament - which is dominated by Remainers and largely opposed to No Deal.
May argued in response that she has won clarifications on the backstop (not enough), published a package of commitments for Northern Ireland (already rejected by the DUP) and plans to give parliament a greater role in the process.
May postponed an initial vote last month in the face of opposition from all sides of the House of Commons, but has now set it for next Tuesday evening after 1900 GMT, following five days of debate which start on Wednesday.
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The talks were extended into an unscheduled third day, showing both sides were "serious", China's foreign ministry said.
A series of MPs rose to complain that the Government motion should not have been amendable.
"So if her deal is defeated next week, as I hope and expect it will, will the Prime Minister do the right thing and let the people have a real say and call a general election?" he added.
"I would suggest to some of my honourable friends - the ones that are getting somewhat overexcited - that perhaps they should don a yellow jacket and go outside", he said.
May has refused to retreat from her unpopular deal, which envisages close trading ties with the European Union after leaving in March. "I think it's those kind of assurances we are happy to give".
Since being elected in 2009, he has angered many Tory MPs for his handling of business and treatment of MPs, but he also has many admirers, particularly on the Labour benches, who believe he has transformed the way Parliament holds the executive to account.
Amid chaotic scenes, Brexiteer former minister Crispin Blunt, warned many no longer regarded him as a neutral arbiter of Commons proceedings and urged him to "reflect" on his position.
"I just invite you to reflect on the conclusion that many of us will have inevitably have come to".
Commons Leader Andrea Leadsom noted there were "some concerns" about Mr Bercow's decision and asked him to confirm that he acted with "full advice" from the Commons clerk and other parliamentary advisers.
"I don't think the British public are served by fantasies about magical, alternative deals that are somehow going to spring out of a cupboard in Brussels", Cabinet Office Minister David Lidington said in an interview with the BBC.