Peers voted in favour of the amendment to the flagship EU Withdrawal Bill by 348 votes to 225, a majority of 123. Another, linked, amendment was approved unopposed.
It seeks to keep open the option of Britain staying in a form of customs union with the EU, something Prime Minister Theresa May is against.
The PM has pledged that Britain will no longer be a member of the bloc’s customs union and single market after Brexit.
She argues this will allow the Government to control immigration and give it more freedom when it comes to negotiating free trade deals with other nations.
Sky’s Political Editor Faisal Islam said the size of the defeat is “bad news” for the Government and suggests there will be many more such amendments when the bill returns to the Commons next month.
A division list analysis shows that 24 Conservative peers backed the amendment, including ex-ministers Lord Heseltine, Lord Lansley and Lord Willetts.
Crossbench peer Lord Kerr of Kinlochard opened the Bill’s report stage by moving the cross-party proposal.
The author of Article 50, the formal mechanism for leaving the EU, argued it was necessary to try and “limit the damage” of the UK severing ties with its largest market.
Brexit minister Lord Callanan said the Government did not support the amendments as it would mean reporting to Parliament on the work taken to deliver an objective it has “clearly ruled out”.
And he hinted that the Government will overturn the measures at a later stage, saying before the vote that Downing Street had no intention to “reflect further” on the issue.
Labour’s Sir Keir Starmer hailed the passage of the cross-party amendment as an “important step forward”.
The shadow Brexit secretary said: “Labour has long championed the benefits of a customs union as the only viable way to protect jobs, support manufacturing and help avoid a hard border in Northern Ireland after we leave the EU.
“Theresa May must now listen to the growing chorus of voices who are urging her to drop her red line on a customs union and rethink her approach.”
The Lib Dems’ leader in the Lords, Lord Newby, described it as a “hugely significant” moment.
“The House of Lords has come together to show the Government that remaining in a customs union is key to the UK’s future prosperity,” he said outside the chamber.
But UKIP slammed the vote as a “clear betrayal” of the more than 17 million people who voted for Brexit in the 2016 referendum.
Leader Gerard Batten said: “Those people did not vote to be half in, half out of the EU. The Commons must reject the Kerr Amendment or put itself in opposition to the people.”
A Department for Exiting the European Union spokeswoman said: “We are disappointed that Parliament has voted for this amendment.
“The fundamental purpose of this Bill is to prepare our statute book for exit day, it is not about the terms of our exit.
“This amendment does not commit the UK to remaining in a customs union with the EU, it requires us to make a statement in Parliament explaining the steps we’ve taken.
“Our policy on this subject is very clear. We are leaving the customs union and will establish a new and ambitious customs arrangement with the EU while forging new trade relationships with our partners around the world.”
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Peers later inflicted a second defeat on the Government after approving amendment 11, which seeks to protect people’s rights after Brexit. They voted in favour of it by 314 votes to 217- a majority of 97.
The Lords will next consider the draft legislation on 23 April.