The government has twice been defeated in the Lords over its Immigration Bill, shortly after losing a vote in the Commons on Sunday trading.
Peers voted to allow asylum seekers the right to work if their claims have not been processed within six months.
They also voted to allow overseas domestic workers to change employers without risking immediate deportation.
Opponents had argued the latter provision would create "a wide open door to the UK" that could be abused.
Peers voted by 280 votes to 195 in favour of a Labour, Lib Dem and crossbench amendment to the Immigration Bill on the rights of asylum seekers to work.
Lord Alton of Liverpool, who proposed it, said it would end the "enforced workhouse destitution" currently experienced by asylum seekers.
"They are frustrated at being forced to remain idle and survive on benefits," he said.
"How many of us could exist on just over £5 a day while an asylum application was being considered? This is way below the poverty line. Where is the justice and fairness in that?"
At present, asylum seekers are not allowed to work unless they have been waiting for a decision on their case for more than a year - and then only in national shortage occupations.
Lord Alton said 3,500 people had been waiting for six months or more by the end of last year, and they deserved to be able to work rather than "eke out" an existence on "pitiful" state benefits.
He insisted "all the available evidence shows that permission to work does not act as a pull factor for asylum seekers, or migrants."
Arguing against the amendment, crossbench peer Lord Green of Deddington warned reducing the time limit could encourage asylum seekers to "spin out" their cases with appeals.
"Not all people seeking asylum are genuine. The record is that 50% turn out not to be. We should be seeking to reduce pull factors, not increase them," he said.
For the government, Home Office minister Lord Bates said the example of Sweden - where asylum seekers can work as soon as they arrive - showed that greater employment rights "might act as a pull factor".
"We should not be doing anything to encourage more people to risk their lives. Now is not the time to make this change," the minister argued.
The second defeat will give domestic workers the right to change their employer once in the UK and to remain in the country for up to two years after doing so.
At present, changing employers is not allowed, but those in favour of the amendment argued that rule often traps individuals in an abusive workplace, as they fear they will be ordered out of the country if they try to leave.
"The scandal of abuse and exploitation has gone on for too long, sometimes in the most affluent parts of London," crossbencher Lord Hylton said.
Opposing the change, Lord Green said it would mean someone could leave their employer whether they were being ill-treated or not, adding: "It provides what will be seen by many as a wide open door to the UK."
Lord Bates said the government was committed to eradicating modern-day slavery and abuse, but argued the amendment could be open to manipulation by people who had not been placed in difficult situations.
Despite those objections, the amendment was supported by 226 votes to 198.