It said the Government should return with a revised European Union exit plan within three sitting days if the Prime Minister's deal is defeated next week.
Nevertheless the vote will be seen as another blow to Mrs May's authority as she struggles to win support for her Withdrawal Agreement.
Corbyn said if May had confidence in her deal, she should "call that election and let the people decide".
MPs are due to vote on her withdrawal agreement on Tuesday night, but it is widely anticipated that it will be defeated, with backbench Brexiteers and the DUP vehemently opposed to both the Northern Irish backstop clause and the £39bn divorce bill.
It could also open the door to alternatives, such as a referendum.
Mr Clark had earlier said that after the Government suffered two Commons defeats over its Brexit plans in the space of 24 hours, it was clear that there was no majority for leaving the European Union without an agreement.
David Lidington, May's effective deputy, called the House of Commons defeat "inconvenient" yet ineffectual and insisted the government remained focused on winning approval for the prime minister's plan.
Alongside the Remain-backing former attorney general in the Aye lobby were former ministers Nick Boles, Kenneth Clarke, Jonathan Djanogly, Justine Greening, Sam Gyimah, Jo Johnson, Phillip Lee, Sir Oliver Letwin, Nicky Morgan, Bob Neill, Anna Soubry and Ed Vaizey as well as Heidi Allen, Antoinette Sandbach and Sarah Wollaston and Brexit-backing Andrew Mitchell.
Mr Grieve's amendment was tabled against a Government motion detailing the timetable for the Brexit deal debate.
The government was defeated on two amendments on Tuesday and Wednesday that curb its powers in the Brexit process, prompting charges that May is in office in Downing Street, but not in power.
He added: 'If we were, as a political class, not to deliver Brexit, that would be a fundamental breach of trust between the people and the politicians.
In a sign of the anger and division Brexit has sown among lawmakers, the motion prompted bad-tempered scenes in Parliament, as Conservatives accused Speaker John Bercow of contravening parliamentary convention by allowing a vote on the amendment.
'That is what I have tried to do and what I will go on doing'.
Justice minister Rory Stewart questioned the basis of Mr Bercow's decision, telling the BBC: "It is a very, very unusual thing that he did".
"We need to act to avoid a no-deal because I don't think there is anything remotely like a majority in Parliament that will tolerate this", he told BBC radio on Thursday.
"I think that is something that we would regret for many, many generations".
So even if he persuades a few wobbly Brexiters to vote with the PM on Tuesday, he has guaranteed that Tory MPs who want a referendum will not be wooed back to her cause.
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.
He said: "If we have a guarantee that works on workers' rights and conditions, that's significant".
"I just invite you to reflect on the conclusion that many of us will have inevitably have come to".
Even the historic defeat for May in the House of Commons Tuesday, when politicians from all parties backed a move aimed at blocking a no deal, has so far failed to change May's resolve.
Greg Clark's comments contradicted official government policy of not ruling out a no-deal Brexit and exposed further divisions after embattled Prime Minister Theresa May suffered a series of setbacks in Parliament.