Following two days of impassioned debate in the House of Lords that exposed deep divisions in the unelected upper chamber, peers voted 390 to 148 against the so-called "wrecking" amendment.
The amendment was a proposal to not allow a second reading of the Marriages (Same Sex Couples) Bill -- a rarely used motion.
The bill is certain to face further stiff opposition during detailed line-by-line scrutiny in its later stages.
The bill has already been backed by the elected lower House of Commons.
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Prime Minister David Cameron is determined to introduce gay marriage as soon as the middle of next year, despite opposition from a hefty chunk of his own centre-right party.
Indeed, the rancour over gay marriage within the Conservative Party has heaped further pressure on Cameron, who is already facing bitter opposition from many Tories over his leadership style and a promised referendum on Britain's European Union membership.
Gay couples in Britain have had the right to enter into a civil partnership since 2005.
In plans unveiled in December, the Conservative-Liberal Democrat coalition government said it was proposing to allow same-sex couples to marry.
However, the plans would explicitly ban the established Churches of England and Wales -- which are opposed -- from conducting ceremonies.
Other religious institutions can "opt in" if they wish.
The other parts of the United Kingdom -- Scotland and Northern Ireland -- have their own law. The Scottish government has confirmed that it will introduce a bill shortly.