She said she managed to reach a hole in the building where rescuers pulled her out.
Reports suggested the death toll was likely to rise.
"We sent two people inside the building, and we could rescue at least 20 people alive. They also told us that at least 100 to 150 people are injured and about 50 dead people are still trapped inside this floor," said Mohammad Humayun, a supervisor at one of the garment factories.
Tens of thousands of people gathered at the site, weeping and searching for family members. Firefighters and soldiers with drilling machines and cranes worked with volunteers to search for survivors.
An enormous section of the concrete structure appeared to have splintered like twigs. Colorful sheets of fabric were tied to upper floors so those inside could climb or slide down and escape.
Rescuers carried the body of a young boy from the building, but it was not immediately clear what he had been doing inside. The building, in the Dhaka suburb of Savar, housed a bank and various shops in addition to the garment factories.
An arm jutted out of one section of the rubble. A lifeless woman covered in dust could be seen in another.
Rahim said his mother and father, who worked with him in the factory, were trapped inside.
Mosammat Khurshida wailed as she looked for her husband. "He came to work in the morning. I can't find him," she said. "I don't know where he is. He does not pick up his phone."
Zahidur Rahman, a spokesman for Enam Medical College and Hospital, said Wednesday evening that 87 people had been confirmed dead. Brig. Gen. Mohammed Siddiqul Alam Shikder said 600 people had been rescued.
The morgue of the medical college echoed with the sobs of people waiting for the bodies of their loved ones. "Where's my mother? Where's my mother? Tell me, tell me, oh Allah, oh Allah!" Rana Ahmed cried.
The November fire at the Tazreen garment factory drew international attention to working conditions in Bangladesh's $20 billion-a-year textile industry. The country has about 4,000 garment factories and exports clothes to leading Western retailers. The industry wields vast power in the South Asian nation.
Tazreen lacked emergency exits, and its owner said only three floors of the eight-story building were legally built. Surviving employees said gates had been locked and managers had told them to go back to work after the fire alarm went off.