Peers voted by a majority of 74 in favour of the amendment, which was not backed by the government, BBC reports, but it is thought to be unlikely that MPs would make any significant changes.
Labour peer Lord Alli proposed the amendment, telling the Lords: "There are many gay and lesbian couples who want to share their civil partnership with the congregations that they worship with.
"And there are a number of religious organisations that want to allow gay and lesbian couples to do exactly that."
It was not an "attack" on the Church of England or the Catholic Church, he added.
Lords leader Baroness Royall and Conservative equality spokesman Baroness Morris of Bolton, a Roman Catholic, both spoke against the amendment but later abstained, the report said.
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