The death toll from the quake rose to 35 earlier on Monday, with more than 100 people still missing.
The quake struck at about 4 a.m. on Saturday (2000 GMT Friday) at the beginning of the Lunar New Year holiday, with almost all the dead found in the toppled Wei-guan Golden Dragon Building in Tainan city.
Rescue efforts are focused on the wreckage of the 17-storey building, where 117 people are listed as missing and are suspected to be buried deep under the rubble.
Wang Ting-yu, a legislator who represents the area, told reporters the woman, Tsao Wei-ling, was found lying under her dead husband. Their 2-year-old son, who was also killed, was found lying nearby.
Another person has also been located, a man called Li Tsung-tian, Wang said. The man is conscious and talking to rescuers.
Tainan mayor William Lai said Tsao and Li were the only signs of life at present, although rescuers were continuing to look for others.
“We have not given up on even the tiniest of possibilities,” he told reporters.
Rescuers continued to scramble over the twisted wreckage of the building as numbed family members stood around, waiting for news of missing relatives.
Lin Tong-meng said he had been waiting at the site for word of his 11- and 12-year-old nephews, who have yet to be found.
“I came back and forth all yesterday and now I’m here again,” Lin said. The boy’s mother and father were rescued soon after the quake. Their father also stood nearby, pacing close to the rubble in tears.
Taiwan’s government said in a statement 33 of the 35 dead were from the Wei-guan building, which was built in 1994.
President-elect Tsai Ing-wen, who won election last month, said during a visit to Tainan there needed to be a “general sorting out” for old buildings to make sure they were able to cope with disasters like earthquakes.
“There needs to be a continued strengthening of their ability to deal with disasters,” she said.
Outgoing president Ma Ying-jeou is also scheduled to visit.
Chinese President Xi Jinping conveyed condolences to the victims, state news agency Xinhua reported late on Sunday, and repeated Beijing’s offer to provide help.
China views self-ruled Taiwan as a wayward province, to be bought under its control by force if necessary.