New gay equality laws which are opposed by the Roman Catholic Church are a "major step forward", the Communities Secretary Ruth Kelly has said.
Gay rights campaigners oppose any exemptions on religious grounds
Peers voted against an amendment to throw out the Equality Act (Sexual Orientation) Regulations, brought by Tory peer Baroness O'Cathain.
Ms Kelly, herself a Catholic, said the measures would deliver "dignity, respect and fairness for all".
The Catholic Church argues the move may lead it to close its adoption agencies.
However the vote, which saw the amendment defeated by 168 votes to 122 in the House of Lords on Wednesday, was hailed by Ms Kelly.
She said afterwards: "This is a major step forward in ensuring dignity, respect and fairness for all.
"These measures will help tackle the practical barriers and real, every day problems faced by lesbian, gay and bisexual people."
Ms Kelly added: "It cannot be right in a decent, tolerant society that a shopkeeper or restaurant can refuse to serve a customer because they are gay.
"It cannot be right for a school to discriminate against a child because of their parents' sexuality or not to take homophobic bullying as seriously as they should."
Among implications of the new laws are that Catholic adoption agencies would be forced to place children with gay couples.
The Catholic Church has said it will be forced to shut its adoption agencies, which handle some of the most difficult-to-place children, rather than act against church teachings.
Some backbench Tory MPs have complained that the draft regulations were being "rail-roaded" through Parliament with "unseemly haste".
Several hundred peers attended the debate. Conservative peers were allowed a free vote as it was an "issue of conscience".
At prime minister's questions earlier, Tony Blair said critics were effectively backing discrimination.
Tory MP Bill Cash told him: "You have given more preference to those who stand for gay rights than those who are concerned with conscience, with family and with religion."
But Mr Blair denied the equality laws were being "rail-roaded" through Parliament, saying there had already been much debate.
The government has refused to grant Catholic agencies an opt-out, but will give them a 21-month transitional period to prepare for the new laws.
The hope is that extra time would allow expertise and knowledge to be passed onto the secular sector, rather than being lost altogether.
Cardinal Cormac Murphy-O'Connor, the most senior Catholic in England and Wales, has said it "remains to be seen" whether the church will cooperate.
Some members of the Church of England's General Synod had written to bishops in the Lords asking them to oppose the measures in Wednesday's debate.
The Equality Act is due to come into effect in England, Wales and Scotland in April.