The upper chamber defied Theresa May, voting by 358 to 256 in favour of an opposition amendment guaranteeing the rights of EU nationals living in the UK after Brexit.
The Government described the result as "disappointing" while sources confirmed they intended to reverse the result when the Bill returns to the Commons.
Despite the setback, ministers are confident they remain on course to meet Mrs May's deadline for invoking Article 50 - marking the start of the formal process of EU withdrawal - of the end of March.
A spokesman for the Brexit Department said: "The Bill has a straightforward purpose - to enact the referendum result and allow the Government to get on with the negotiations."
With seven rebel Conservative peers voting for the amendment along with 78 independent crossbenchers, opposition parties urged ministers to take the opportunity to rethink their position on EU nationals.
For Labour, shadow Brexit secretary Sir Keir Starmer said EU nationals should not be used by ministers as "bargaining chips" in the forthcoming Brexit negotiations.
"There is a growing consensus that this must be resolved before Article 50 is triggered, and the Prime Minister is now increasingly isolated," he said.
However there was anger among some pro-Brexit MPs at the vote after the elected House of Commons passed the Bill - which allows minister to trigger Article 50 - without amendments.
Labour MP Gisela Stuart, who co-chaired the official Vote Leave campaign, said :"The British people voted in their millions to leave the EU, and their elected MPs passed the Article 50 Bill without amendment.
"The House of Lords should do the same and not seek to frustrate the Brexit process."
Conservative Theresa Villiers, the former Northern Ireland secretary who campaigned for Brexit, said there was wide sympathy for the position of EU nationals but the Bill was "not the right vehicle" to resolve it.
The Government argued that while it wanted to secure the future rights of EU citizens in the UK, it needed to be able to secure reciprocal rights for British citizens living in the EU at the same time.
The Bill is now expected to return to the Commons on March 13 and 14 where a similar amendment was defeated by the Government.
If MPs again reject the amendment it will then "ping pong" back to the Lords where senior opposition peers have indicated they will not seek to defeat the Government again, potentially allowing Mrs May to invoke Article 50 on March 15.
The impassioned and at times angry three-hour debate in the Lords exposed divisions within Conservative ranks over Mrs May's Brexit strategy.
Former cabinet minister Douglas Hogg, now Viscount Hailsham, urged peers to take the "high moral ground" and offer reassurance to the millions of EU citizens who had made their home in the UK.
However another Conservative cabinet veteran Lord Tebbit sparked jeers when he said the debate seemed to focus on "nothing but the rights of foreigners".