A rescuer told the The Telegraph he had been in the search party which found the woman under tumbled concrete pillars.
Didar Hossain said: "The lady who gave birth to a baby boy was rescued on Wednesday after six hours.
"She gave birth while inside the building. She was about 26 or 27 years old. When we found her, she said: 'Please save my baby first'."
He said she did not appear to have suffered any serious injuries and was taken out of the debris, reunited with her relatives and taken to her family home.
"The baby was crying. The umbilical cord was still there. After bringing them out we placed the baby in a cloth. There were other women around who took the responsibility to cut the umbilical cord."
Her tale of survival and miracle birth was one of a number of extraordinary escape stories. A group of 40 survivors were discovered alive after they had been trapped for more than 72 hours trapped in temperatures of 95F (35C) and without food or water. Some went to their homes, rather than to hospital.
"They were not injured much but of course they had became very weak," said one of the rescuers.
The government has postponed plans to turn the rescue mission into a clearance operation using heavy machinery to clear the dead bodies and rubble.
Officials believed that the victims would not be able to survive for more than 72 hours after the collapse, but relatives and rescuers are convinced there may be more people still trapped alive.