Ministers saw off a move to give MPs the decisive say on what happens over Brexit if they do not agree with the deal negotiated by the United Kingdom government.
Leading Conservative rebels welcomed the "important concessions" by the government, but insisted that ministers must follow through on their concession or face a defeat when the bill returns to the House of Commons later this month.
The Lib Dems, who identify strongly as an anti-Brexit party to the point of pushing for a second referendum and running by-elections in Remain-friendly seats on that platform, opposed the Government.
The pound strengthened 0.3 percent against the dollar to $1.3424 after parliament voted to back the government on several amendments to the European Union withdrawal bill.
Overall MPs voted against the House of Lords' amendments in three separate votes.
"The government have conceded that this is necessary and I expect to see a new amendment to cover this situation soon".
"I think it would be fairly certain that one of the members of the House of Lords would find a way to put down Dominic's original wording, that couldn't be voted on yesterday. It is, however, irresponsible to proceed as we are". It meant that the United Kingdom government successfully defeated the Lords amendment, 324 to 298, to the dismay of Labour and other opposition parties.
But ministers now know that a narrow but decisive Commons majority can be assembled against them on critical Brexit issues, and that its next outing could well be on a more substantive vote on a customs union.
The government says lawmakers should be offered a choice only between its final deal and no deal at all.
"I trust our PM to honor the undertaking she gave", said Anna Soubry, one of the pro-EU Tory rebels.
The government's compromise is that a minister would come to the House within 28 days of a deal being rejected to tell MPs what will happen next.
"The Brexit secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of parliament and government in negotiating global treaties, and respecting the referendum result".
The concession seems to be a victory for the Remain camp and last night Tory Brexiteers were concerned the climbdown could damage the prime minister's ability to walk away from the negotiations if the European Union offer was not good enough.
He confirmed that ministers will seek to overturn 14 amendments which he said would undermine the objective of the Bill and fail to respect the result of the 2016 referendum.
The cumulative effect of 14 Lords amendments which the Government is seeking to overturn could be to "make it impossible to deliver the smooth and orderly exit we want", he warned.
But it seems a threatened rebellion may have been seen off by a last-minute compromise amendment reached between Remain and Leave supporting MPs calling for "a customs arrangement".
Her fellow Conservative backbencher Stephen Hammond said: "Parliament must be able to have its say in a "no deal" situation".
It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
Government sources signalled to the Press Association that ministers were set to back the move.
MPs will on Wednesday debate a series of other amendments to the bill, which if passed, would seek to force May to change course and negotiate to stay inside a customs union and the single market after Brexit.