Brexit Bill clause passed without Holyrood's consent
The SNP says not enough time was given to debate the parts of the Bill about devolution.
The EU Withdrawal Bill has been passed by MPs despite the Scottish Parliament denying the legislation its consent.
Its contentious clause 15 will see some powers held by the EU not immediately passed to Holyrood despite coming under devolved policy areas.
The SNP and Labour criticised the UK Government's programme motion for the Commons debate on the Bill, which meant less than 20 minutes was allocated to discussing the devolution amendment.
MPs voted by 321 to 40 to agree with the remainder of amendments made by the House of Lords, which included devolution.
Among those voting in line with the Theresa May's government were Scotland's 13 Conservative MPs, while all bar two MPs in Jeremy Corbyn's Labour party opted to abstain.
It comes after MSPs from the SNP, Labour, the Liberal Democrats and the Greens united at Holyrood to formally deny the UK Bill legislative consent last month.
Tuesday's Commons vote marks the first time since devolution began that a Bill has been passed at Westminster against the formal wishes of the Scottish Parliament.
Ian Blackford, the SNP's leader at Westminster, said: "We are witnessing the biggest ever attack on devolution with Scotland's voice silenced by the Tories.
"Events in Westminster have been absolutely outrageous.
"The Tories campaigned against the Scottish Parliament in 1997 and now they are actively dismantling it - they really think they can do anything they want to Scotland and get away with it.
"For Labour to abstain on a devolution vote is gob-smacking. It is a complete dereliction of duty from the so-called party of devolution."
He continued: "The Tory power-grab would keep devolved powers including on farming, fishing, environmental protection, food standards, and labelling coming back from Brussels, centrally in London.
"As the First Minster has said, Scotland now faces 'an unprecedented constitutional position, which puts at risk 19 years of constitutional convention and practice, on which devolution relies.'"
The party's deputy leader at Westminster Kirsty Blackman raised frustrations about the length of time taken between each amendment as MPs filed into Westminster's voting lobbies to make their choices.
At the Scottish Parliament, voting is carried out electronically within the chamber.
Blackman told STV News: "We voted against the programme motion because we didn't believe there was enough time for debate. We were right."
She added: "The archaic voting system is even more of a problem when it eats into the time for debate.
"This is not how democracy should be done."
Labour's shadow Scotland secretary Paul Sweeney also criticised Conservative ministers, saying "insufficient parliamentary time" had been allocated for discussion of issues related to the devolved administrations.
He added that his party's decision to abstain in the vote on the amendments was made because to vote against them would have meant "defaulting back to the original draft of the EU Withdrawal Bill, which was even worse".
The Bill has long been dubbed a "power grab" by the Scottish Government.
However, while initially joined by the Welsh Government, Cardiff eventually reached a deal with UK ministers following amendments to the legislation.
Secretary of state for Scotland David Mundell commented: "The EU Withdrawal Bill provides certainty for business and families in Scotland as we leave the EU.
"It fully respects both the spirit and letter of the devolution settlement.
"It guarantees the vast majority of powers returning from the UK will go directly to Edinburgh, Cardiff and Belfast.
"In a small number of areas current arrangements will remain in place until we can create new UK-wide frameworks."
The Tory minister continued: "We have made strenuous efforts during a year of negotiations to reach agreement with the Scottish and Welsh governments.
"We are disappointed the Scottish Government did not support it, as the Welsh Government has done."
Scottish Conservative MP Paul Masterton added: "The Welsh Government agreed to the government's new plans.
"By contrast, Nicola Sturgeon's government hasn't budged an inch. There's a reason why: she never wanted a deal on this, she wanted a fight. It's pathetic.
"We know that Nicola Sturgeon just wants to pick a fight and concoct another reason for another independence referendum.
"With the SNP - everything is always about independence. That is the sad reality.
"When even Donald Trump and Kim Jong Un can do a deal, perhaps it's time the Nationalists admit they've got this wrong."
Scotland's Brexit minister Michael Russell, in his own statement, said UK Government had "(torn) up the constitutional rulebook" and imposed its will on the Scottish Parliament.
He said: "Further Brexit bills will also require the consent of the Scottish Parliament - and yet the UK Government has decided to use this moment to tear up the rules that have until now protected devolution.
"We will reflect on this situation carefully as we consider our next steps."
Speaker of the House John Bercow took points of order from SNP, Labour and Tory MPs for more than 50 minutes after the votes on the devolution and Northern Ireland amendments.
Earlier, Theresa May's government staved off defeat on the flagship Bill with last-minute concessions which could give MPs a bigger say on the final withdrawal agreement, making a "no-deal" exit much less likely.
MPs voted by 324 to 298 to reject a House of Lords amendment to the legislation which would have given MPs the power to tell the Prime Minister to go back and renegotiate the Brexit deal.