Speaking hours before the vote, Mr. Corbyn told BBC Radio4's World at One programme that staying in the EU Single Market is "open for discussion".
But lawmakers voted by 318 to 301 to support the so-called program motion, which sets out the timetable for the remaining stages of the bill's progress through parliament's lower House of Commons.
The Brexit bill will formally end Britain's EU membership and overturn the supremacy of European law in the country.
Members of Parliament passed the European Union (Withdrawal) Bill - which will transfer EU law into United Kingdom legislation when Britain exits the bloc - by 326 votes to 290.
It will repeal the 1972 act taking Britain into the European Economic Community and convert EU law into United Kingdom law.
According to May's government, the bill will allow them to make minor technical changes to ensure a smooth transition process.
"In recent years, the European Union has helped achieve crucial foreign policy goals - from bringing Iran to the negotiating table, to uniting in response to Russian aggression in Ukraine".
Shadow Brexit Secretary Keir Starmer said the bill was a "naked power grab" by the government, adding that "this is a deeply disappointing result".
"Labour will seek to amend and remove the worst aspects from the bill but the flaws are so fundamental it's hard to see how this could ever be made fit for objective", the Labour MP said.
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 Davis said before a parliamentary vote.
Mrs May says she needs the broad powers in the law because hundreds of British laws will need to be corrected to remove references to the European Union after Brexit.
The paper also offers to agree joint foreign policy positions with Brussels, including cooperating on global sanctions against states or terrorist organisations.
"It's in our mutual interest to work closely with the European Union and its member states to challenge terrorism and extremism, illegal migration, cyber crime, and conventional state-based military aggression", he said.
OXFORD'S MPs voted against the Government's bid to extract the United Kingdom from European Union law in time for Brexit.