Theresa May headed off defeat in the crunch Commons clash and hailed results as a historic Parliamentary victory that would allow exit negotiations to move on.
Jeremy Corbyn had branded the European Union (Withdrawal) Bill a ministerial “power grab” and ordered his MPs to vote against the Government.
But seven Labour MPs backed giving the Bill a second reading and 13 abstained in the vote, although at least one missed the debate as a result of hospital treatment.
Labour former minister Caroline Flint defied the three-line whip to abstain, accusing opponents of the repeal Bill of wanting to “thwart the result of the EU referendum and prevent or delay the UK leaving the EU”.
Smaller parties attacked the rebels for walking “hand in hand” with the Tories to give the Government extreme powers and warned the party to “get their act together”.
The Bill will transpose relevant EU law on to the UK statute book to ensure there are no gaps in legislation at the point of Brexit.
The vote allowing it to move on to the next stage in Parliament passed by a comfortable majority of 36, which included all 10 of the DUP MPs that are propping up the minority government.
No Conservatives opposed the move but five, as well as two Tories acting as tellers, did not walk through the voting lobbies.
Mrs May said: “Earlier this morning Parliament took a historic decision to back the will of the British people and vote for a Bill which gives certainty and clarity ahead of our withdrawal from the European Union.
“Although there is more to do, this decision means we can move on with negotiations with solid foundations and we continue to encourage MPs from all parts of the UK to work together in support of this vital piece of legislation.”
Labour said the results were “deeply disappointing” and the Liberal Democrats described it as “a dark day for the mother of parliaments”.
Shadow Brexit Secretary Keir Starmer said the Bill was a “naked power grab” by the Government.
“This is a deeply disappointing result,” he said.
“This Bill is an affront to parliamentary democracy and a naked power grab by Government ministers. It leaves rights unprotected, it silences Parliament on key decisions and undermines the devolution settlement.
“It will make the Brexit process more uncertain, and lead to division and chaos when we need unity and clarity.
“Labour will seek to amend and remove the worst aspects from the Bill as it passes through Parliament. But the flaws are so fundamental it’s hard to see how this Bill could ever be made fit for purpose.”
Tom Brake, Lib Dem Brexit spokesman, said MPs who backed the Bill should feel “ashamed”.
“They have abdicated their responsibility to scrutinise legislation and relinquished parliamentary sovereignty to Theresa May’s unrepresentative cabal.
“This is a dark day for the mother of parliaments. The Liberal Democrats will fight to amend the Bill in committee to stop this affront to democracy.
“Labour rebels have handed the Government sweeping anti-democratic powers. A significant number walked hand in hand with the Tories and have given the Government extreme powers not seen since the Middle Ages.”
Plaid Cymru said divisions in the Labour Party “risk letting the Tories off the hook” while the SNP claimed the Scottish Tories had abandoned Scotland’s “economic and social interests and instead followed Westminster orders”.
Some Tories had called for extra time to be granted to allow MPs to assess flagship Brexit legislation line by line.
But MPs approved the timetable guaranteeing 64 hours of debate by a majority of 17 after Justice Secretary David Lidington said the Government is “willing to consider” giving more time to the next stages of the Bill if there is “good reason”.
An earlier bid by Labour to block the Bill was defeated by 318 votes to 296.
Conservative Mark Harper said: “Those in the Labour Party who voted against this Bill have shown themselves to be more concerned with playing party political games than securing the best Brexit possible for the UK.”