MPs backed a plan put forward by Mr Sunak that will see the commitment to spend 0.7% of national income on aid restored only when the public finances improve.
Critics of the move warned there was no guarantee the conditions set by the Chancellor would ever be met.
MPs voted by 333 to 298, a majority of 35, to back the reduction in aid funding from 0.7% of gross national income (GNI) to 0.5% – a cut equivalent to around £4.4 billion this year.
Former leader of the Scottish Conservatives, Ruth Davidson retweeted a message saying that the vote had lead to a ‘big Tory rebellion’ saying: “Not big enough.
"For colleagues' who stood on manifesto after manifesto committed to this, it's a bloody disgrace.”
Ruth Davidson’s tweet was picked up by Scottish Health Secretary Humza Yousaf, who commented: “That would be you Douglas Ross.
“Ruth is right, you and your Tory colleagues should be ashamed, a disgrace.”
All of the Scottish Conservative MPs voted to support the move, including Douglas Ross, the current leader of the Scottish Conservatives.
Former prime minister Theresa May, one of 24 Tories to join opposition parties in voting against the cut, warned that some of the world’s poorest people will die as a result of the decision to slash spending on overseas aid.
She added that the cut meant the Government “turns its back on the poorest in the world”.
“This isn’t about palaces for dictators and vanity projects, it’s about what cuts to funding mean – that fewer girls will be educated, more girls and boys will become slaves, more children will go hungry and more of the poorest people in the world will die,”
The commitment to 0.7% is written in law and restated in the 2019 Conservative manifesto, but was ditched as the Government attempted to save money in response to the economic carnage caused by coronavirus.
Mr Sunak said: “Whilst not every member felt able to vote for the Government’s compromise, the substantive matter of whether we remain committed to the 0.7% target – not just now but for decades to come – is clearly a point of significant unity in this House."