Members of Parliament's upper chamber voted to postpone in two separate motions meaning the government will have to put together analysis to find out how working families will be affected before any changes can be made.
Some reports claimed millions would lose on average of £1,300 a year.
Peers would not usually vote down economic measures like this in the House of Lords as they tend to back an elected government, however Labour and the Liberal Democrats chose to take action to put a stop to the changes.
The Church of England bishops also put down a motion declaring their disappointment, but allowing the cuts to complete their parliamentary passage.
Speaking about the delay, James Mildred from the Christian charity CARE, said: "This is a body blow for the government.
"We believe the tax credit changes they were proposing were deeply misguided and would cause financial misery for many hardworking families so this really is a reality check for the Chancellor."
Chancellor George Osborne has criticised the intervention by peers.
Speaking after the vote, he said: "David Cameron and I are clear that this raises constitutional issues that need to be dealt with.
"However, it has happened, and now we must address the consequences of that. I said I would listen and that's precisely that I intend to do.
"I believe we can achieve the same goal of reforming tax credits, saving the money we need to save to secure our economy, while at the same time helping in the transition.
The President of the Liberal Democrats, Baroness Sal Brinton, who's also a chair of the group Christians in Parliament, told Premier before the vote how it was vital that the changes were stopped.
She said: "If we don't stop this dead, the poorest working families in this country are going to be severely affected."
Listen to James Mildred speaking to Premier's Aaron James.
Listen to Bishop Christopher Foster speaking to Premier's Martyn Eden before the vote.
Listen to Baroness Brinton speaking to Premier's Marcus Jones before the vote.