MPs backed the Internal Market Bill by 340 votes to 263.
As the Government's internal markets bill passed the first vote in the Commons last night, James O'Brien branded the news an "astonishing U-turn".
The main battleground in the next four days of debate is likely to be an attempt by Bob Neill, a Conservative lawmaker, to amend the bill to give parliament, not ministers, the power to decide whether to overrule the Brexit treaty.
A wrecking amendment, which would have deleted the Northern Ireland provisions, was also defeated late on Monday night.
The bill is created to enable goods and services to flow freely across England, Scotland, Wales and Northern Ireland when the United Kingdom leaves the EU's single market and customs union on 1 January 2021.
"The breaking of the law ultimately leads to very long-term and permanent damage to this country's reputation".
Former Labour leader Ed Miliband went off on UK Prime Minister Boris Johnson over his controversial Brexit bill, bashing him for "incompetence" and "failure of governance".
Ahead of the vote, Mr Johnson urged MPs to back the Bill saying it was a "safety net" that would "guarantee the economic and political integrity of the United Kingdom".
Johnson, though, said it was essential to counter "absurd" threats from Brussels including that London put up trade barriers between Britain and Northern Ireland and impose a food blockade - steps he said threatened the UK's unity.
Sajid Javid, Conservative MP and the previous Chancellor of the Exchequer (finance minister, in other words), had also come out against the bill, saying in a tweet that he could not see why it would be necessary to break worldwide law in the instance of the Internal Market Bill.
The Northern Ireland Protocol, created to prevent a hard border returning to the island of Ireland, was negotiated and agreed by Johnson last autumn.
He acknowledged some personal "unease" at giving ministers powers to override the Brexit treaty but said they would not be needed if a trade deal was agreed as hoped with Brussels.
There will be more parliamentary skirmishes in London, which will embarrass Mr Johnson, but opponents concede that he has the numbers to push the measure through the lower House of Commons.
With Starmer self-isolating after being told this morning that a member of his household was showing possible symptoms of Covid-19, the Shadow Business Secretary and former party leader opened the debate for Labour. Should the Lords oppose the bill, they could delay it by one year.
"Either he wasn't straight with the country about the deal in the first place or he didn't understand it", Miliband said.
"Understandably the European Union sees the Internal Market Bill as a direct breach of the Northern Ireland protocol which was designed to prevent a hard border on the island of Ireland at the cost of creating a customs border in the Irish Sea".
"It is critical that we pass this Bill before the end of the year".