They were plucked to safety from the upstairs of the property in Jamaica Street just before midnight on Thursday.
The cause of the blaze – which started in the kitchen – is still under investigation.
Local people tried to rescue the family but were beaten back the intensity of the fire and thick black smoke.
Local Paul Savage said he and other neighbours tried their best.
“We got into the front hall but the smoke was so black we couldn’t see up the stairs.
“Then the fire brigade and paramedics came and did their job.”
The alarm was raised by a taxi driver and within minutes 20 firefighters and three ambulances arrived.
Fire crews with breathing apparatus pulled the parents and the baby girl out of the two storey house.
Paramedics then got to work to keep the unconscious trio alive.
William Johnston from the fire service said the fire was “well developed” on the ground floor when they arrived.
“There were lots of neighbours in and around the area who were alerting the crews to some personnel trapped within the house,” he said.
“We removed the casualties from the premises and the fire crews worked with the paramedics to look after them.
“They were unconscious at the time and were taken to the Royal Victoria Hospital by the paramedics.”
Police have issued an appeal for information.