It was passed by 413 votes to 202 - a majority of 211.
Downing Street said the government was still preparing for a no-deal Brexit.
If she is to win, one leading indicator could be whether the 10 DUP MPs, who prop up her minority government, also get behind her deal.
DUP deputy leader Nigel Dodds said lengthy talks on Friday with senior ministers including Chancellor Philip Hammond were "constructive" and there was a "renewed focus" from the Government on addressing their concerns.
It has been a bruising week for the Prime Minister, with her Cabinet in open revolt as the focus on her leadership intensified.
Hastings and Rye MP Amber Rudd has written a letter to her constituents to explain why she chose to abstain from last night's vote on ruling out a no deal Brexit.
PA Theresa May faces another difficult night
If the deal is rejected by MPs again, Mrs May has warned that the EU is likely to only accept a longer delay, which would mean the United Kingdom would need to send new MEPs back to the European Parliament.
Her authority hit an all-time low this week after a series of parliamentary defeats and rebellions.
If passed, it will order Theresa May to seek to delay Brexit "for the purposes of legislating for and conducting a public vote in which the people of the United Kingdom may give their consent" for either leaving the European Union on the terms of a deal agreed by Parliament or remaining in the bloc.
May's government and her Conservative Party are divided and discipline has frayed, with several ministers refusing to back the government's line in voting.
European Union leaders will consider pressing Britain to delay Brexit by at least a year to find a way out of the domestic maelstrom, though there is shock and growing impatience at the political chaos in London.
"You don't just have a short, technical extension to our membership of the European Union, you nearly certainly need a significantly longer one to find a time for parliament to come to a majority verdict", he told BBC radio.
German Justice Minister Katarina Barley said Britain must use any extra time productively.
He added: "I will have a chance to speak to him in more detail at that point and I would hope that things over the next couple of days may become a bit clearer in terms of what Westminster wants and what the British Government wants". But these are no ordinary times and it will be up to the speaker of the house to decide whether or not to allow such a vote to go ahead.
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