Earlier, a medical team had provided the woman with an intravenous drip of glucose, and rescuers had been able to speak with her through a gap in the debris.
"The medical team has administered IV, glucose has been administered," said Pisu Masai, the head of the National Disaster Management Unit.
"She is talking and in good spirits ... we are taking our time to ensure she is removed safely," he added before the successful rescue.
A nearly six-month-old baby was rescued unharmed on Tuesday, raising hopes that more survivors could be found. Rescuers have so far rescued a total of 137 people, including the woman freed on Thursday.
Official put the death toll from the disaster variously at 35 or 36, and 70 people are still missing, according to the Kenya Red Cross.
Unscrupulous methods
The building in Nairobi`s Hururma district collapsed on Friday night after days of heavy rain. The Interior Ministry said the building had been earmarked for demolition but that local authorities had failed to act on the order.
The National Construction Authority found in an audit last year that more than half of buildings in Nairobi were unfit for habitation. The recent collapse is only the latest in several such disasters over the past years.
The city is struggling to keep up with demands for housing, and some unscrupulous developers are taking advantage of the haste to save money and maximize profits by bypassing regulations.
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