The issue of a "meaningful vote" is set to be a flashpoint in the Commons, with ministers seeking to overturn a Lords amendment which would give Parliament extensive powers to direct ministers how to proceed if a deal with Brussels is rejected by MPs or no deal is reached.
In a rare alliance, senior Tory Remain and Leave MPs have urged party rebels to back Prime Minister Theresa May on the bill.
Earlier May suffered a setback when junior justice minister Phillip Lee, who has always been critical of Brexit strategy, resigned and said he would vote against the government.
He accused the Government of trying to "limit" Parliament's role and called for another referendum once ministers' chosen path becomes clear.
She has already agreed to give MPs a vote on the final Brexit deal, but says it will be a yes or no decision - meaning that rejecting it could see Britain crash out of the EU.
This assurance was enough to convince Tory rebels to vote with the government.
Earlier this year, Lee had called on the government to release its economic impact assessments of Brexit and suggested the government change tack in talks with the European Union, underlining the deep rifts in his party over the best way to manage Britain's exit.
The key vote which has taken place is whether MPs will have a "meaningful vote" - amendment 19 proposed by the Lords - on the final Brexit agreement.
In a presentation published on its website on Monday, the European Commission set out a series of concerns it has about the U.K.'s proposal, which Britain says should replace the EU's plan that keeps only Northern Ireland in the European customs union and parts of the single market.
After the resignation of justice minister Phillip Lee, who said he could not support the government's position on Brexit, it was said government whips feared a Tory rebellion on the "meaningful vote" amendment passed by the House of Lords.
In the event, Dr Lee abstained on the crucial vote, saying he was "delighted" the Government had agreed to introduce an amendment giving Parliament "the voice I always wanted it to have in the Brexit process".
Opening the debate, Brexit Secretary David Davis insisted the government would abide by three principles to defend the will of the British people.
And to avoid a sudden "cliff edge" on Brexit day, 29 March 2019, it would also convert existing European Union law into United Kingdom law so the government and Parliament can decide at a later date which bits they want to keep or change.
He said a concession of this kind would been "revolutionary" as the Commons can not override the government when it came to negotiating worldwide treaties.
Theresa May saw off a revolt from the pro-European wing of her fractured party, averting what could have been a major political crisis.
Mrs May's concession to Parliament means that lawmakers now have more power if she fails to secure a Brexit deal, which may lead to a softer approach to Britain's divorce.
Brexit protesters outside Parliament House.