The government has avoided by a whisker a defeat in its customs legislation after accepting the demands of the Brexiteers to change their wording.
After a reaction by EU Tories, who accused Theresa May of "surrendering" to the Euro-skeptical MP, she survived twice with only three votes.
Defense Minister Guto Bebb resigned to vote against the government.
MEPs will discuss Brexit on Tuesday, when the commercial code will be received by the Municipalities.
It offers the government the opportunity to build new business relationships around the world after the UK left the EU, and MEPs who support the EU customs union try to change their formulation.
Critics have said that the amendments of the Eurosceptics to the Customs Act on Monday would have undermined Britain's recently announced negotiating position.
But Downing Street, which had previously agreed to accept the four amendments, said it was "consistent" with the White Paper, outlining how it intends to negotiate with the EU in the coming years.
The United Kingdom will leave the EU on March 29, 2019, but still has to agree on how its final report will work with the EU.
The government, which does not have a majority in the House of Commons, has been pressured by parliamentarians on both sides in the Brexit debate.
This was emphasized on Monday when he accepted for the first time a series of requests from the Brexiteers who are dissatisfied with the White Paper's proposals because they believe that Britain remains too tied to the EU.
But this irritated the party's pro-EU deputies, who refused to support the new amendments, which led to heavy exchanges in the lower house when the Customs Law was discussed.
Pro-EU MEP Anna Soubry has suggested that the controversial Euro-skeptic Jacob Rees-Mogg will now "reign Britain".
"This government is in grave danger not only of losing the plot, but also of losing the support of people in that country, unless we have done well at Brexit," he said.
Another Remainer, the former Attorney General Dominic Grieve, said that the Prime Minister "took a position of considerable weakness" by adopting the amendments.
He added that the political system in the country was "torn" by Brexit and that a second referendum could be necessary if the deputies failed to reach a consensus on this issue.
What the Members voted for
Rees-Mogg said the amendments are "largely in line" with government policies and the government has accepted them.
With 305 votes in favor – including 14 rebel rebels – MEPs supported an amendment that prevents the UK from imposing taxes on behalf of the EU, unless the rest of the EU does not do the same for the UK.
The application of EU tariffs to EU products is part of Ms. May's plan to avoid friction at the British border after Brexit.
Another amendment to ensure that the UK is outside the EU VAT system was supported from 303 to 300 with a Tory rebellion of 11.
Three Labor MPs voted with the government.
The government won several more votes in a more convenient manner, and the entire bill was then approved by the lower house with 318 to 285.
BBC political editor Laura Kuenssberg
It looks very messy because it's a mess. It is becoming increasingly difficult for the Prime Minister to get results through Parliament – and while a second, largely rejected referendum is being asked, this sentiment could change if this kind of stalemate persists.
The prime minister has spent the last two years making compromises. He has a divided party and no majority. There are no easy decisions.
But the Tory party's divisions reduce their maneuvering space on a daily basis. In a political debate, the problem for some is that the compromise is a dirty word.
Read Laura's blog
Who has rebelled?
The three Labor MPs who rebelled against their party leaders by voting with the government were Frank Field, Kate Hoey and Graham Stringer – all pro-Brexit.
The former Labor MP Kelvin Hopkins, who now sits as an independent, also supported the government in one of the amendments.
The conservative rebels were pro-EU parliamentarians for a long time: Ken Clarke, Heidi Allen, Guto Bebb, Richard Benyon, Jonathan Djanogly, Dominic Grieve, Stephen Hammond, Philip Lee, Nicky Morgan, Robert Neill, Mark Pawsey, Antoinette Sandbach and Anna Soubry Sarah Wollaston.