He proposed an alternate agreement that would give ministers seven days to come up with new terms if Parliament chose to veto the final Brexit deal, and give the government until November 30 to reach a new deal.
Mr Grieve confirmed he voted with the UK Government after receiving assurances, telling Sky News: "I am quite satisfied we are going to get a meaningful vote".
Following a five-hour debate, MPs reinstated the precise day the United Kingdom will leave the European Union - 29 March 2019 - in the proposed legislation while backing an amendment on the Irish border, guaranteeing there will be no new border arrangements without the agreement of the United Kingdom and Irish authorities.
Scottish Government ministers and SNP MPs were outraged when amendments to the EU Withdrawal Bill related to devolution were passed by the House of Commons after just 15 minutes of debate - with Cabinet Office Minister David Lidington the only member who made a speech.
The government on Thursday published detailed plans for a so-called "temporary customs arrangement" with the EU.
"The British people voted to leave the European Union, and as prime minister I am determined to deliver that", May told parliament. But Britain's second, unelected, lawmaking chamber attached various amendments, including one of a "meaningful parliamentary vote" on the deal. The Prime Minister seems to have averted disaster for her government this week - but maybe only this week.
And senior pro-EU Tory Dominic Grieve withdrew his own amendment, which would have given MPs powers to dictate what the Government should do if no acceptable agreement is reached by February 2019.
Mrs May has promised to give the British Parliament a vote on the final deal, but the question is what happens if lawmakers decide to reject it.
Potential rebels fell into line after Solicitor General Robert Buckland said ministers were ready to "engage positively" with their concerns before the Bill returns to the Upper House next Monday.
The Prime Minister has sought to reassure Brexit supporters that the concessions do not amount to handing the Remainer-dominated Parliament an effective veto over the Brexit deal - or Brexit itself.
Conservative former minister Anna Soubry said the abuse of MPs who speak out against the government's Brexit policy "simply has to stop".
French foreign minister Jean-Yves le Drian said all sides should set themselves a clear deadline of next month to come to a decision.
The government's eleventh hour amendment, lifted in large parts from Tory Remainer Dominic Grieve's own proposal and to be presented to the Lords on Monday, is expected to give MPs the right to veto the government's strategy if it fails to secure a political agreement with the European Union by 30 November.
But the resignation by Phillip Lee, who has always been critical of the government's Brexit strategy, underlined the deep rifts in the party over Brexit that makes such votes anything but easy.
Davis warned lawmakers the government would never allow them to "reverse Brexit" and called on them to back its own amendment, which proposes a 28-day breathing space if parliament rejects a Brexit deal, during which the government would have to make a statement on its plans.