She condemned the government for refusing to wait until the Lords committee had reported before introducing the regulations.
Peers voted by a majority of 120 to extend the type of research allowed on early-stage embryos, and in so doing opened the way for researchers to practise a limited form of human cloning.
The move followed fears that the Lords would refuse to back the changes and would delay the introduction of the new regulations for at least a year.
Many peers had been against the measures because of the concern that they would bring reproductive human cloning - making whole copies of people - one step closer.
Some just wanted to delay the introduction of the changes until a Lords committee had examined all the issues.
But after eight hours of debate on Monday, the House agreed to back the new regulations. It also voted to set up the special committee, although this will not delay research.
Government pledge
The government has pledged to take the committee's recommendations into account when it reports later this year. However, this is unlikely to satisfy critics such as Conservative Baroness Cox.
She condemned the government for refusing to wait until the Lords committee had reported before introducing the regulations.
"The United Kingdom is now out on a moral limb," she said. "A momentous decision was taken on an unamendable regulation before parliament was able to be fully informed by a very detailed consideration by a select committee. It is putting the cart before the horse."
But Labour MP and a member of the Commons Science select committee, Ian Gibson said the vote would help to further science in the UK.
"We are right up front in advancing scientific research for the benefits of our people and indeed across the world.
"I think we are at the stage now with science where certainly using embryonic stem cells we can start to ask real questions."
'Morally right'
The vote was also welcomed by Liberal Democrat science spokesman Evan Harris.
"I am personally delighted - and that delight will be shared by patient groups and clinicians - that the Lords have done the morally right thing.
"That is to allow carefully regulated research on stem cells using early embryos to proceed in the search for cures for some terrible diseases."
Scientists developing treatments for a number of diseases have also welcomed the vote.
Dr Austin Smith, from the Genome Research Centre at Edinburgh University, said the decision was good news.
"If the Lords had taken an alternative decision, it would have been a devastating blow, principally for the patients who suffer from diseases like Parkinson's and diabetes for which stem cell research offers hope."
'A worrying step'
However, a leading expert on ethics in the field, Dr Tom Shakespeare, said it was a worrying step.
"We are very concerned about using embryos in this way, using them as a means to an end," he said. "There are actually things we can do with adult stem cells, so there are alternatives to this technology.
"There are very many reasons why we are going too fast and should be much more cautious about this development."
Scientists believe that many serious, degenerative diseases, such as Alzheimer's and heart disease, and even spinal cord injuries, could be cured if they can develop new ways to regenerate or replace damaged tissue.
Many believe that the best hope for this lies with the stem cells present in a growing embryo. These cells have the ability, under the right conditions, to generate virtually all the tissues in the body.
If the stem cells are sourced from an embryo made from the patient's own genetic material, the new tissues would be a perfect match and would not be rejected by the immune system.
This would allow patients to get on with their lives free from the restrictive drug regimes current transplant patients have to endure.