The amendment to exclude child benefit from the cap was carried by 252 votes to 237.
Labour peers, cross benchers and 24 rebel Liberal Democrat peers, including former party leader Paddy Ashdown, were among those voting for the amendment, which had been put forward by bishops.
The government said the amendment effectively raises the cap to such a level that it becomes irrelevant and has pledged to plough on with its plans when the bill returns to the House of Commons.
A DWP spokesperson said:"There has to be a limit on the amount of money benefit claimants can receive. We think that limit is set at a fair rate of £26,000, the equivalent to someone earning £35,000 before tax, a salary that many working families would be happy to receive.
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