Peers have amended the government's Trade Bill again, as they hope to stop deals being done with countries who have committed genocide.
The bill has gone back and forth between Lords and MPs due to a row over the best way to tackle the issue.
The government got the backing of MPs - despite a Tory rebellion - to give select committees a greater role in examining allegations of genocide.
But Lord Alton wants claims looked at by people with judicial experience.
Speaking in a debate on the bill in the House of Lords, the crossbench - or independent - peer said: "We failed to predict genocide, we failed to prevent genocide, we failed to protect victims of genocide and we failed to prosecute perpetrators of genocide.
"The genocide amendment is a modest attempt to begin to address some of those failings."
But Trade Minister Lord Grimstone said the government's existing plan was a "reasonable, proportionate and substantive compromise" that would "ensure that the voice of parliament is to be heard".
Despite his plea, peers backed the new amendment by 367 votes to 214 - a majority of 153 - and it will now go back to the Commons for MPs to look at.
A number of MPs, including many Conservative backbenchers, have been pressing the government to take a tougher stance on human rights abuses - especially in light of the treatment of the Uighur Muslim population in China.
The House of Lords backed a previous amendment put forward by Lord Alton to give British courts the right to decide if a country was committing genocide - which would then impact the decision over whether to sign a trade deal with them.
His proposal got the public backing of a number of Conservative MPs and looked set to lead to a rebellion in the Commons.
But the government used parliamentary procedure to prevent MPs voting on the amendment and instead managed to secure enough support for its own measure.
This would allow a parliamentary committee to trigger a Commons debate and vote if it decided there were "credible reports" that genocide had been committed by a state the UK was negotiating a trade deal with.
Lord Alton had been expected to re-table his proposal as the bill returned to the House of Lords - in a process known as "ping-pong" - but he instead put forward a new one.
His latest amendment would keep the select committee report on genocide as the first step, but it would then be referred to a panel of five MPs and Lords who had held "high judicial office" in the past - such as former High Court or Court of Appeal judges.
During the debate, Lord Alton accused the government of "total inadequacy" on its response to genocide.
He said peers would send the "strongest possible message that this House will not remain indifferent or silent to the very worst atrocity crimes nor will your lordships be satisfied with a slight of hand".
Conservative, Labour, Liberal Democrat and Green Party peers all spoke to back the amendment, praising Lord Alton for "doing the right thing".
Lord Grimstone praised the "powerful and reasoned" debate, but he said existing actions by the government - including targeted measures on supply chains - were already demonstrating the "reputational and economic costs to human rights violations".
He called on peers to "rally around the sensible amendment" agreed in the Commons rather than backing the new one.
But instead, peers backed Lord Alton's amendment and it will now return to the Commons again for another vote.