But the battle has only just begun. The Human Fertilisation and Embryology Bill is set to spark heated debate on either side when it returns to the House of Commons for its second reading.
MPs voted on Monday evening by 340 votes to 262 in favour of sending the bill to its committee stage where they will argue the ethics behind stem-cell research as well as the legal limit on abortion.
Votes on amendments to the bill - which will include proposals to lower the legal abortion limit to 16 or 18 weeks from 24 weeks - will happen in the next few weeks in the Commons.
Prime Minister Gordon Brown, facing a potential cabinet revolt and intense pressure from the Roman Catholic church, agreed in March to give Labour MPs a free vote on the "ethical" aspects of the bill.
These include a provision to allow the creation of human-animal embryos, a move to allow so-called "saviour siblings" - creating a sibling through IVF to treat a child with a life-limiting condition - and the removal of the requirement for doctors to consider "the need for a father" when offering fertility treatment.
Although the bill makes no reference to abortion, pro-life MPs are tabling amendments proposing the legal limit be reduced.
Scientists say embryo research using hybrids will give them the large numbers of embryos they need to make stem cells to help find cures for diseases.
Sufferers of conditions like motor neurone disease or Parkinson's argue that all avenues must be pursued to find treatment or possible cures but opponents say the research is immoral and tampers with the laws of nature.
Researchers create inter-species hybrids by injecting human DNA into a hollowed-out animal egg cell. The resulting embryo is 99.9 percent human and 0.1 percent animal.
Britain is one of the leading states for stem cell research, attracting scientists from around the world with a permissive environment that allows embryo studies within strict guidelines.
The Human Fertilisation and Embryology Authority, which regulates the research, gave permission to two groups of British-based scientists to use hybrids in January.
The House of Lords rejected attempts earlier this year to include a ban on hybrid research in the draft legislation.
