She was shifted to a hospital immediately after being rescued and her condition was stated to be stable, the official said.
Director General of Police, Fire Service, B K Sharma said fire personnel from Bamur and Angul took part in the rescue operation along with several others under close supervision of senior officers.
Chief Minister Naveen Patnaik congratulated the fire service staff and ODRAF team for their "wonderful work" of successfully rescuing the girl, an official in the chief minister's office said.
"Heartiest congratulations to all whose sincere efforts led to the rescue of 3-year-old Radha Sahu from inside the borewell hole in Angul district," Sharma said.
A parallel hole of 15-16 feet depth was dug nearly 6 feet from the borewell hole and then a tunnel was dug to connect to the borewell, he said in a Twitter post.
Once the tunnel opened to the borewell, a fireman reached and carefully rescued the child, the official said.
Meanwhile, the district administration of Angul has ordered an inquiry into the incident.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)