Normally, a woman with an ectopic pregnancy would present with severe pain and bleeding in the first few weeks after conception.
But Ms Cahill said Mrs Thangarajah had experienced no symptoms, and the abnormality did not show up on a pre-natal scan.
She said only 1 in 40,000 fertilisations implant in the ovary, and it was unheard of for one of those foetuses grow to full term. But despite those statistics, Durga - meaning Goddess - was born at 38 weeks weighing 6lb 3oz (2.8 kg).
"We're calling it a miracle," Ms Cahill said.
Risk of bleeding
The Royal College of Obstetricians and Gynaecologists said the odds of survival in such a pregnancy were "no more than one in a million".
Spokeswoman Dr Maggie Blott said: "One that goes to produce a live healthy baby is very unusual.
Dr Blott on the rare occurrence of full-term ectopic pregnancies
"There is a great risk in such a pregnancy of bleeding.
"And had it been picked up at six to eight weeks, it would have been removed because of the risk to the mother.
"This type of pregnancy is very rare indeed."
Obstetrician Dr Andrew Miller, who delivered Durga, told AFP news agency that he had not realised there was a problem until he saw the ovary stretched almost to breaking point.
"And you can't believe that the baby, just by normal movement, wouldn't have caused the sac [inside the ovary] to rupture," he said.
"It was so paper thin you could see the baby's hair."
The baby's father, Ravi, told local television that doctors had told him: "You're one of the luckiest men in the world at the moment."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.