The bill would the government to trigger Article 50 of the European Union's Lisbon Treaty and formally begin two years of Brexit negotiations. The bill now moves to committee for further scrutiny.
Prime Minister Theresa May's plan to take Britain out of the European Union easily cleared its first legislative hurdle on Wednesday, paving the way for the government to launch divorce talks by the end of March.
The House of Commons decisively backed the bill by 498 votes to 114, sending it on for committee scrutiny.
May's government is seeking approval for a new law giving her the right to trigger Article 50 of the EU's Lisbon Treaty - the legal process for leaving the bloc - after the Supreme Court ruled she could not take that decision without consulting parliament.
May wants to begin exit negotiations with the EU by March 31, starting two years of talks that will define Britain's economic and political future and test the unity of the EU's 27 remaining members.
The bill could complete the legislative process by March 7. Wednesday's vote sends the bill to the next, more detailed legislative stage.
Parliament rejected an attempt to throw out the bill, proposed by pro-EU Scottish nationalists. They described the vote as "a devastating act of sabotage on Scotland's economy."
A majority of voters in Scotland and Northern Ireland in last summer's referendum backed remaining in the EU, while voters in England and Wales supported Brexit.