74 Labour MPs voted in favour of the amendment, despite Mr Corbyn urging his colleagues to abstain.
"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process".
Two more contentious bills - on trade and customs - are set to be debated before parliament breaks off for its summer recess, and pro-EU rebels are poised for a series of fresh confrontations, including over membership of the customs union.
Losing the vote in the Commons would have spelt serious trouble for Mrs May, whose position as prime minister was weakened past year when she lost her parliamentary majority after calling a general election.
It was always doomed to fail because it was opposed by the Labour party.
In the tense atmosphere where it was not clear which way the vote would go, the government secured its victory only after offering concessions to one of the leaders of a group of Conservative lawmakers who were threatening to vote against May.
Downing Street insisted today it will not accept a compromise tabled by former Cabinet minister Dominic Grieve, which would force the government to come up with a new strategy in the event of the Brexit deal being rejected, and put that to MPs again for approval.
Lawmakers will vote on Wednesday on whether to dismiss a plan proposed by the upper chamber of parliament which would require ministers to report what efforts they had made to secure a customs union with the EU by the end of October.
"If we don't achieve a deal at all, the fact is we are going to be facing an enormous crisis", he told MPs.
Anti-Brexit MPs had argued that removing the no-deal outcome was necessary for the vote to be a meaningful one.
LONDON - Theresa May is risking a major parliamentary defeat on Brexit which could bring down her government, after pro-EU Conservative rebel MPs accused her of breaking her promise to offer Parliament a veto on leaving the EU without a deal.
Theresa May's landmark Brexit legislation returns to the House of Commons on Tuesday, with the 15 amendments added to it by the upper House of Lords mostly created to keep closer ties to the European Union and give Parliament more power over the divorce process.
The chances of the government being defeated when the Bill returns to the House of Commons later this month has now risen significantly, with trust between May and her MPs at an all-time low.
There is little May can do.
May, who leads a minority government propped up by the small Northern Irish Democratic Unionist Party (DUP), conceded that "we need parliamentary support" to implement Brexit.
Tory whips are particularly anxious about the so-called "meaningful vote" amendment, with rumours that concessions last week could be pushed further.
Mrs May is coming under increasing pressure from European Union negotiators to come up with detailed positions not only on customs, but also on future trade relations and governance.
On Tuesday the government also saw off other potential rebellions earlier this week which threatened to derail its Brexit plans.