A number of Tory MPs had tabled amendments, but they were rejected during the five hour debate.
Minister Robert Jenrick says he’ll engage with any MPs who believe it violates human rights laws.
The plans stop anyone who comes to the country illegally from claiming asylum.
Tooting Labour MP Dr Rosena Allin-Khan voted against the bill, saying “it takes away vital support for trafficking victims and fails to tackle smuggling gangs”.