An unnamed 21-year-old woman presented herself to doctors at the Ram Snehi Hospital, in Jahazpur, after experiencing pain during her pregnancy.
She was immediately referred for a sonography scan and an ultrasound and were told that she was carrying twins - but were unaware they would be parasitic.
Unlike conjoined twins, one is incompletely formed or wholly dependent on some bodily functions of the complete foetus.
Cases of parasitic twins are rare and believed to account for just one per one million live births, according to medical literature.
Dr Vijiyeta Garg, a gynaecologist who looked after the woman, assured the family that both mother and child could be saved.
However, her 24-year-old husband, who works as a farmer, insisted that her life was a priority and the baby should come second.
After a successful Caesarean section, the family were relieved that both managed to survive before the child was referred to JK Lone Hospital - 540km away.
The operation on April 26 proved to be a success - despite the young couple believing they would lose their first child, local reports suggest.
Dr Pravin Marthur, of the hospital's paediatric unit, said: "This is one of the rarest cases of parasitic twin.
"The parents told us the mother had undergone sonography and other tests but were not told about carrying an underdeveloped twin.
"They were shattered when they saw the baby. We had to convince them to give us a nod for the surgery to save their daughter's life.
"After immediate consultation with a team of radiologist and support from assistant professors, we successfully removed the head from the viable child."
The hospital did not charge the family for any health or surgery costs. The baby is recovering well and is being breastfed and will be discharged later this week.
Parasitic twins are usually a result of a delay in the separation of embryos during conception.
They are formed when one embryo maintains a dominant development at the expense of the other.
