The operation in the CURE International Center for Orthopedic Specialties in the Dominican Republic began on Friday morning and was expected to last up to 15 hours.
The baby, Rebeca Martinez, was born in mid-December at a hospital in Santo Domingo with the head of an undeveloped twin attached to the top of her skull, facing upwards.
The infant is otherwise healthy but her brain cannot develop normally unless the undeveloped head is removed.
The operation is being led by Dr Jorge Lazareff, director of pediatric neurosurgery at UCLA's Mattel Children's Hospital, and Dominican surgeons Dr Santiago Hazim and Dr Benjamin Rivera.
Lazareff led the surgical team that successfully separated Guatemalan twin girls conjoined at the head last year.
Iranian sisters Laleh (R) and
Ladan Bijani died after surgery
Hospital director Ruth Taveras Brito said the $100,000 operation was free for the parents, Maria Gisela Hiciano and Pablo Martinez.
The baby girl's condition, cranio pagus parasiticus, is so rare there have been only eight documented cases in the world, and no known cases where surgery has been attempted to correct it.
Conjoined twins form when an embryo begins to split into identical twins and then stops, leaving them fused.
Twins conjoined at the head account for about one of every 2.5 million births and about 2% of all conjoined births.
Pressure on brain
Rarer "parasitic" twins occur when one conjoined twin stops developing in the womb, leaving a smaller, incomplete twin that is dependent on the other.
They can form as an extra limb, torso or head, or as a complete second body, lacking vital organs.
In Rebeca's case, there is a gap in her skull where the heads are joined, and the blood vessels are intertwined.
The vestigial head is enlarged and fringed with dark hair like Rebeca's, but has a poorly developed brain and only rudimentary facial features.
Rebeca was born weighing about 3.2kg and now weighs more than 4.5kg, but the undeveloped head is drawing away nutrients and exerting pressure on her brain.