It came after Brexit minister Steve Baker warned pro-Remain MPs not to think they could keep Britain in the EU by stealth through tinkering with crucial exit legislation.
In the first of a series of crunch votes, MPs backed repealing the 1972 European Communities Act which brought Britain into the bloc on January 1, 1973.
They voted by 318 to 68, majority 250, for repealing the Act, which gives EU law supremacy over UK law.
Repealing it is the first clause of the EU (Withdrawal) Bill which aims to provide an orderly Brexit, regardless of the outcome of talks with Brussels about an exit agreement.
MPs backed repealing the Act of Parliament which made European Union law supreme over Britain's
The Bill will transfer EU regulations into British law on exit day, to ensure legal continuity for firms and people when Britain leaves, while Parliament can then decide which to keep, amend or scrap.
The Commons yesterday held the first of eight days of intense debate on the detail of the Bill, which MPs have tabled hundreds of amendments to, and which will later have to go to the House of Lords for consideration.
Mr Baker told the Commons that scrapping the 1972 Act "could scarcely be more significant.
"It is a historic step in delivering our exit from the EU in accordance with last year's referendum.
Conservative MP Steve Baker
"If we were not to repeal the Act, we would still exit the EU at the end of the Article 50 process from the perspective of EU law but there would be confusion and uncertainty about the law on our own statute book.
"It would be unclear if UK or EU law took precedence.
"The status of new EU law would also be unclear."
The 1972 Act meant the rights and obligations contained in EU laws automatically applied in the UK without the need or ability for the UK Parliament to refuse or approve, he said.
Repealing it would end "one of the widest-ranging powers ever placed on the statute book of the UK and makes it clear and unarguable that sovereignty lies here in this Parliament".
Pro-Brexit former minister John Redwood told the House: "This simple, crucial clause is the way in which our democracy is completely restored and once it has gone through, any matter that worries the British people can properly be the subject of Parliamentary debate and decision.
"This Parliament once again can hear the wishes of the British people and can change things – our VAT, our fishing policy, our agricultural policy, our borders policy, our welfare policy – in the ways that we wish."
Mr Baker stressed the Government seeks a Brexit deal with the EU in the two-year talks Theresa May triggered in March by invoking Article 50 of the EU treaties, after Parliament agreed she could do so.
But senior Labour MP Yvette Cooper's call for separate legislation specifying "exit day" and to approve any final deal, was a recipe for "legal chaos" if it were not passed by Brexit day on March 29, 2019.
Senior Labour MP Yvette Cooper
Mr Baker warned: "No-one should fall into the trap of thinking this would keep us in the EU if no withdrawal agreement were concluded.
"We would leave under Article 50 and the treaties would no longer apply but our domestic law would be in an unfit state and we could have legal chaos.
"As a responsible government we must be ready to exit without a deal even though we expect to conclude a deep and special partnership."
He urged MPs when they get the chance on a future occasion, probably next month, to back a Government amendment to the Bill specifying 11pm on March 29, 2019 as the point Britain leaves the EU.
'This crucial clause is the way in which our democracy is completely restored', said John Redwood MP
Labour and some Tories say putting a date in law is too restrictive and would stop Britain extending talks if necessary to reach a deal with Brussels.
Pro-European Tory former minister Ken Clarke told the Commons Mrs May was just trying to appease pro-Brexit ministers and the move was "ridiculous, unnecessary and could be positively harmful to the national interest".
He ironically hailed former Ukip leader Nigel Farage as the "most successful politicians of my generation" for persuading people to believe "myths" that the 1972 Act caused "faceless, grey eurocrats to produce vast quantities of awful legislation and red tape" and that they could now "look forward to having bent bananas again once we repeal it".
Labour Shadow Brexit Secretary Sir Keir Starmer said writing Brexit day into law was a "desperate gimmick" by Mrs May trying to keep her eurosceptics in line.
MPs voted by 318 to 68, majority 250, for repealing the Act
Pro-Brexit Tory Bernard Jenkin told the House: "Any MPs who voted for Article 50 but then do not want to fix the date are open to the charge that they don't want us to leave the EU."
Pro-EU Tory former minister Anna Soubry heckled him: "Bernard, you're a disgrace."
Labour MP Frank Field said he wanted March 30, 2019, named as Brexit Day, enabling Britain to leave "on British time", not "at the beckoning of the Europeans" given that 11pm British time is the Continent's totemic midnight.
Meanwhile many Tory MPs are fuming after a "stormy" meeting on Monday with new Chief Whip Julian Smith where they say he implied people trying to amend the EU (Withdrawal) Bill were actually trying to stop Brexit.
Mrs May warned last week that she will 'not tolerate' attempts to use the Bill to slow down Brexit
They insist they accept the referendum result but are trying to ensure a good deal.
Mrs May's warning last week that she will "not tolerate" attempts to use the Bill to slow down or block Brexit is also seen by many of her own MPs as a "gratuitous threat".
In the first vote of the Withdrawal Bill's committee stage, MPs voted by 318 to 52 votes, majority 266, against a demand by nationalist parties that the legislation cannot take effect unless the devolved parliaments of Scotland, Wales and Northern Ireland consent.