It twice made due by only three votes after a reaction from master EU Tories who blamed Theresa May for "collapsing" to the gathering's Eurosceptic MPs.
Resistance Minister Guto Bebb surrendered so he could vote against the administration.
MPs will bear on debating Brexit on Tuesday when the Trade Bill goes to the Commons.
It enables the administration to construct new exchange connections around the globe after the UK leaves the EU, and MPs who bolster remaining in the EU's traditions association are trying to change its wording.
MP Guto Bebb stops as clergyman after Brexit vote
MPs to vote on late-spring break
Brexit: All you have to know
Pundits said the corrections to the Customs Bill set around Eurosceptics on Monday would undermine the UK's as of late reported arranging position.
In any case, Downing Street, which concurred prior to acknowledging the four corrections, said they were "reliable" with the White Paper where it sets out how it needs to exchange with the EU in years to come.
The UK is because of leave the EU on 29 March 2019 yet still can't seem to concur how its last association with the alliance will work.
The administration, which does not have a Commons larger part, has been experiencing strain from MPs on the two sides of the Brexit talk about.
This was underlined on Monday as it initially acknowledged a progression of requests from Brexiteers who are troubled at the recommendations in the White Paper, trusting it keeps the UK too firmly fixing to the EU.
Be that as it may, this incensed MPs from the gathering's master EU wing who declined to back the new changes, prompting warmed trades in the House of Commons as the Customs Bill was wrangled about.
Media captionAnna Soubry censured associates who have a "gold-plated annuity" and bolster Brexit
Genius EU MP Anna Soubry recommended backbench Eurosceptic Jacob Rees-Mogg was presently "running Britain".
"This administration is in grave risk of not simply losing the plot but rather losing a lot of help from the general population of this nation except if we get Brexit right," she said.
Another Remainder, previous Attorney General Dominic Grieve, said the head administrator had, by tolerating the corrections, place herself in "a place of significant shortcoming".
He included that the political framework in the nation was "being torn separated" by Brexit and a second submission might be required if MPs couldn't achieve an agreement on the issue.
What the MPs voted on
Mr. Rees-Mogg said the corrections were "extensively in line" with government strategy, which is the reason the legislature acknowledged them.
By 305 votes to 302 - with 14 Tories revolting - MPs upheld a revision that keeps the UK from gathering charges for the benefit of the EU, except if whatever remains of the EU does likewise for the UK.
Applying EU levies to items bound for the EU is a piece of Mrs. May's arrangement to maintain a strategic distance from grating at UK fringes after Brexit.
Another change, to guarantee the UK is out of the EU's VAT administration, was upheld by 303 to 300, with a Tory resistance of 11.
Three Labor MPs voted with the legislature.
The administration won a few different votes all the more serenely, and the whole bill was then endorsed by the House of Commons by 318 to 285.
No place to a move
BBC political supervisor Laura Kuenssberg
It looks a wreck since it is a wreck. It's getting increasingly hard for the head administrator to get things through Parliament - and keeping in mind that requires a second submission are broadly dismissed, that supposition could change if this sort of gridlock proceeds.
The PM has put over the most recent two years attempting to trade off. She hosts an isolated get-together and no dominant part. There are no simple decisions.
Yet, the divisions in the Tory party are day by day diminishing her space for the move. In a level-headed discussion about the guideline, the issue for some is that trade-off is a grimy word.
Read Laura's blog
Who revolted?
The three Labor MPs who defied their gathering whip by voting with the administration were Frank Field, Kate Hoey, and Graham Stringer - every one of whom is star Brexit.
Previous Labor MP Kelvin Hopkins who currently sits as a free additionally upheld the administration on one of the changes.
The Conservative renegades were the long-term master EU MP Ken Clarke, Heidi Allen, Guto Bebb, Richard Benyon, Jonathan Djanogly, Dominic Grieve, Stephen Hammond, Philip Lee, Nicky Morgan, Robert Neill, Mark Pawsey, Antoinette Sandbach, Anna Soubry and Sarah Wollaston.
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