Helpfully for her, seven Labour lawmakers disobeyed their own leader Jeremy Corbyn's orders to vote against the bill, while another 17 abstained.
The bill also would end the jurisdiction of the European Court of Justice, which ensures that law.
On Monday MPs backed the EU Withdrawal Bill by 326 votes to 290.
The Bill will repeal the 1972 act taking Britain into the European Economic Community and transpose relevant EU law on to the United Kingdom statute book to ensure there are no gaps in legislation at the point of Brexit.
Theresa May's plans for taking Britain out of the European Union remain on track after members of Parliament cleared the way for her Brexit law to advance - but threatened to re-write it later.
"Parliament has already voted to leave the European Union".
The government claims it needs the power to be able to make minor technical changes to ensure a smooth transition.
It is controversial because it hands sweeping powers to ministers to change legislation as they see fit, without full scrutiny in Parliament.
May's Conservative government secured parliamentary approval for the bill thanks to its alliance with Northern Ireland's Democratic Unionist Party (DUP).
"This bill is an affront to parliamentary democracy and a naked power grab by government ministers".
Britain faces a chaotic exit from the European Union if lawmakers vote against legislation created to sever political, financial and legal ties with the bloc, Britain's Brexit minister David Davissaid before a parliamentary vote.
In its latest Brexit position paper, Theresa May's government will call for a pooling of British and European Union assets and capabilities in a security partnership "deeper than any other third country and that reflects our shared interest".
The Government is also offering to agree joint foreign policy positions with Brussels, including co-operating on worldwide sanctions against states or terrorist organisations.
Members of both parties said they'd seek changes to the bill after entering the committee stage, with pro-European Tories such as Dominic Grieve, Nicky Morgan and Anna Soubry indicating that they would vote for the bill with later amendments in mind, and pro-Brexit Labour lawmakers Kate Hoey and David Stringer, and former European Minister Caroline Flint saying they'd break ranks to back the bill.
Timo Werner talks up potential transfer
Discussing teammate Naby Keita's move to Liverpool next summer, Werner added: "There's no anger to him". RB Leipzig are "confident" that star striker Timo Werner will be staying .