The Safety of Rwanda Bill passed its third reading in the Commons unamended with a majority of 44.
Eleven Tories, including former home secretary Suella Braverman, voted against Mr Sunak's immigration plan - despite other would-be rebels indicating they opposed the legislation before the vote.
Serious opposition is now expected as the bill moves to the House of Lords - prominent peer Lord Carlile, a former independent reviewer of terrorism legislation, has said that the legislation represents “a step towards totalitarianism”.
Mr Sunak's bill states that Rwanda must be treated as a "safe country" under UK law, which the government believes will allow deportation flights to the country to begin.
Lord Carlile told BBC Radio 4’s Today programme: “We’ve seen in various countries the damage that is done when governments use perceived and often ill-judged political imperatives to place themselves above the courts – this is a step towards totalitarianism and an attitude that the United Kingdom usually deprecates."