She said unless there was a "meaningful vote" Parliament would be left with "the grim choice between a poor deal and exit with no deal at all".
It is not clear what the rebels may have been offered by the Whips behind closed doors to persuade them to toe the party line.
Dismissing claims that Mrs May had effectively abandoned her threat that the United Kingdom could leave the European Union without a deal, Mr Jenkin said: "There is only agreement for discussions, not concessions".
For now, May saw off a revolt that would have challenged her authority at a time when she is increasingly under pressure to move ahead with all-but-stalled Brexit talks in Brussels by offering a more detailed plan.
Around a dozen Tory Remainers said that May had promised them that the government would accept two parts of the amendment by Grieve, a former attorney general: a vote on the final deal and a statement from ministers to seek approval from parliament for the next steps if no deal is reached by November 30 of this year.
Dr. Sarah Wollaston, chair of the heath select committee, switched to back the Government after saying she was "minded" to rebel over voting against the Lord's amendment.
It followed a strained parliamentary session, where the deep nationwide divisions opened up by Britain's vote to leave the European Union in 2016 were on display, with pro-EU lawmakers saying they had received death threats.
It is expected that Tuesday will see MPs decide whether Parliament should have the power to set the Government's negotiating goals if Theresa May's deal with Brussels is voted down.
Remainer Stephen Hammond said a group of potential rebels - believed to number 15-20 - received assurances from the PM moments before the key vote.
Instead, the government has proposed reporting its efforts to secure a customs arrangement.
After days of frantic lobbying by Conservative officials to try to get the party on board, May renewed appeals for unity over the "meaningful vote", after the government appeared to have secured a compromise to stop a similar rebellion on Wednesday over Britain's trading ties with the EU.
"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process", Davis said.
"We are asking members of parliament to abide by the referendum result, our manifesto commitment and to back our country", Andrew Bridgen, Conservative lawmaker and Brexit campaigner, told Reuters. The text needs to honor her pledge to pro-EU Tories that she'll take account of their concerns over the possibility of leaving the bloc without a deal.
The problem for the prime minister is that she can't keep both sides happy.
Labour MPs are expected to rebel against their party whip in significant numbers to vote in favour of a Lords amendment to keep the United Kingdom in a Norway-style trading arrangement post-Brexit.
There is little May can do.
"This isn't about narrow party politics", she told BBC Radio 4's Today programme.
Often she simply puts off votes that could end in embarrassing defeats.
No. There will be plenty more chances for upsets as separate Bills on customs and trade come before MPs next month, followed by legislation on future immigration rules later in the year and a Withdrawal Agreement and Implementation Bill once the final Brexit deal is struck.