498 voted in favour of giving the Bill a second reading, with 114 against, with a majority of 384 backing the Bill.
MPs clashed during two days of debate over the European Union (Notification of Withdrawal) Bill.
Prime Minister Theresa May told MPs earlier that the vote to give the Bill a second reading would decide whether to deny the will of the British people.
The legislation allows the Prime Minister to decide when to trigger Article 50 and begin the two-year process of negotiation on Brexit.
Around 90 MPs were expected to vote against the bill – including around 48 Labour rebels.
Shadow home secretary Diane Abbott, a close ally of Mr Corbyn, did not vote.
A Labour source said she was “taken ill” and left Parliament at about 5pm.
Labour rebel Ben Bradshaw said: “This is the single most important issue of any our lifetimes.”
He said he was “really worried about the implications of a hard Brexit.”
Speaking after the vote, Ken Clarke said “the battle has only really just begun”.
Mr Clarke is the only Tory to vote against the Bill.
The SNP-led plot to derail Brexit was foiled as Article 50 cleared its first hurdle in Parliament in a major blow to Nicola Sturgeon.
336 MPs voted against the amendment with 100 for the SNP amendment.