Peers have rejected government plans to limit to five days the time failed applicants have to appeal to the new asylum and immigration tribunal.
Asylum campaigners welcomed the climbdown on the right to appeal
The House of Lords voted by 143 to 94 to back a Lib Dem amendment which doubled the appeal period to 10 days.
The government is now considering whether to try to overturn the changes in the House of Commons.
Immigration Minister Des Browne accused the Conservatives of hypocrisy and opportunism over the defeat.
Later, peers mounted a second defeat against the government when they said lay people should assess appeals alongside the judge heading the tribunals.
Ministers believe only a judge is needed because appeals decide points of law, but the Tories and Lib Dems changed the plans by 151 votes to 98.
Constitutional Affairs Secretary Lord Falconer has pledged the reformed appeal system will be fair and fast.
But his plans have proved controversial and he has already backed down over a proposal to deny failed asylum seekers the right to appeal to the High Court.
Lord Falconer told BBC Radio 4's Today: "What we have tried to do is introduce measures that mean the process by which you look at claims is fair but it's fast as well."
He added: "We listened to what people have said. We've introduced an element of High Court supervision that we think deals with the very points that have been made about the detail of the scheme."
The most senior judge in England and Wales, Lord Woolf, had said Lord Falconer's proposals over limiting court supervision would go against the basic principle of the rule of law.
Opposition to the original proposal had come from the Law Society, the Bar Council and Justice as well as senior judges all of whom had called for the plans to be abandoned, warning they could cost lives.
In Monday's debate, Liberal Democrat spokesman Lord Goodhart said: "Unfortunately the government's proposals while plainly swift, are blatantly
It was unrealistic to expect people to be able to prepare for appeals in advance because judgements were not so predictable, he argued.
But the immigration minister said the latest defeats showed the Tories once again failing to back up "tough rhetoric" on asylum with action in the Lords.
Mr Browne said: "Why do they think that asylum seekers who have lost their appeal having been
represented by highly qualified lawyers should be given more than five days to challenge the final stages of the process?
"This is hypocrisy with a capital 'H'."
Peers are looking at the government's Asylum and Immigration Bill as part of its House of Lords report stage.