MPs have backed Sir Oliver Letwin's cross-party Brexit indicative votes plan by 329 votes to 302, inflicting a defeat on the government.
The success of the Letwin amendment paves the way for a series of "indicative votes" in the Commons on Wednesday, effectively taking control of the Brexit process out of the hands of the Government.
The rebellion against the government was helped by the resignations of Foreign Office Minister Alistair Burt and pro-EU business minister Richard Harrington.
The vote against Theresa May came after she ruled out a third vote on her Brexit deal on Tuesday.
ITV News Political Editor Robert Peston declared the PM's Brexit authority "in tatters" after the result.
Mrs May earlier confirmed she still doesn't have enough support for a third meaningful vote after the DUP told ITV News: "Nothing has changed."
Despite her failure to gain support for her deal, the PM said she would "continue to have discussions with colleagues across the House to build support so that we can bring the vote forward this week and guarantee Brexit".
As well as the Letwin amendment, the Speaker also selected Amendment D, tabled by Labour, and Amendment F, which was put forward by Dame Margaret Beckett.
The Labour amendment was later held before the MPs broke to vote at 10pm.
Video report by ITV News Political Correspondent Paul Brand
In a statement to the Commons Mrs May said the "default outcome" remained leaving without a deal and said "the alternative is to pursue a different form of Brexit or a second referendum".
Labour leader Jeremy Corbyn, responding to Mrs May's update to the Commons, said: "The government's approach to Brexit has now become a national embarrassment."
He also confirmed his party will back the Letwin amendment for indicative votes on Brexit, telling the House of Commons: "It is time for Parliament to take control."
Mrs May said she could not guarantee that she would commit to implementing anything MPs voted for in an indicative process, saying the result could "lead to an outcome that is un-negotiable with the EU".
"No government could give a blank cheque to commit to an outcome without knowing what it is," she said.
She added: "The bottom line remains: if the House does not approve the Withdrawal Agreement this week and is not prepared to countenance leaving without a deal, we would have to seek a longer extension."
That would mean holding European elections and would mean "we will not have been able to guarantee Brexit", she said.
Mrs May said she regretted having to delay Brexit beyond the scheduled date of March 29.
But she cautioned MPs against seeking to obstruct a statutory instrument tabled on Monday which will remove the date from Brexit legislation, warning that this would "cause legal confusion and uncertainty but it would not have any effect on the date of our exit".
ITV News Political Correspondent Paul Brand summed up the day's key moments in a tweet that showed just how quickly the government's position on a third meaningful vote (MV3) had changed.
It came after the European Commission warned no-deal Brexit on April 12 is becoming "increasingly likely", adding that its preparations for that outcome are now complete.
The warning followed a difficult weekend for the PM in which there had been reports Cabinet members were planning to oust her.
Secretary of State for Wales Alun Cairns denied anyone had called for her to resign during Cabinet called by the PM ahead of a historic week of crunch votes which could shape the outcome of Brexit.
At the start of another crunch week in Westminster, the Commons is due to vote on an amendment which would force a series of indicative votes on alternatives to the Prime Minister’s Withdrawal Agreement.
Defeat for the government on Monday night on the plan – tabled by former ministers Sir Oliver Letwin and Dominic Grieve and Labour MP Hilary Benn – would be a further humiliation for Mrs May.
The proposal seeks to pave the way for a series of indicative votes in the Commons on Wednesday, effectively taking control of the Brexit process out of the hands of the government.
Brexit Secretary Steve Barclay warned the risk of a general election would increase if MPs took control of parliamentary proceedings and brought about a "constitutional collision".
But Chancellor Philip Hammond said "one way or another" MPs would be given the opportunity this week to decide what it is in favour of, though could not confirm whether Tories would be given a free vote on the options.
In a statement released by the European Commission, it said it had completed its preparations for a possible no-deal Brexit, but warned it would nonetheless cause "significant disruption for citizens and businesses".
If it crashes out without a deal on April 12, the UK will not benefit from a transition period to new arrangements, but will immediately be subject to checks and tariffs on its exports to the EU, while "significant delays" can be expected at the borders, said officials.
Mrs May is preparing to update the Commons on the Brexit process following last week’s European Council summit where she agreed to delay Britain’s departure beyond March 29.
It comes after a weekend which saw two senior ministers dismiss reports of a “coup” to oust the PM.
The Sunday Times reported 11 Cabinet ministers had told the paper they wanted Mrs May to make way for someone else and that the PM's de facto deputy David Lidington was in line to take over the helm as a caretaker prime minister until a leadership contest could be held.