Ayse Yildiz and her child Nusra had spent 28 hours trapped in the rubble in the eastern city of Elazig following Friday’s 6.8-magnitude quake.
Rescue teams heard their cries several hours before they were able to reach them, with night-time temperatures dropping as low as -5C.
A total of 45 survivors had been rescued by Sunday morning, according to Turkey’s Disaster and Emergency Management Authority.
The agency also confirmed that the death toll had risen to 38 with more than 1,600 injured, of whom 13 were in intensive care, although none were in critical condition.
More than 700 aftershocks rocked the region as 3,500 rescuers searched for more survivors with the help of 19 dogs and five drones. A 4.3-magnitude earthquake also hit neighbouring Malatya province on Sunday morning.
“It has been around 36 hours [since the earthquake], but we are still in the hours where we can hope,” Turkey’s minister of the interior, Suleyman Soylu, told a news conference in Elazig.
At least 76 buildings were demolished and 645 seriously damaged, according to a survey of the damage in the provinces of Elazig and Malatya.
More than 4m Turkish lira (about £500,000) of emergency aid has been sent to the governors of the region, along with more than 7,500 tents, 11,500 beds and 18,720 blankets.
The Turkish Red Crescent has sent thousands of food parcels to the area, as well as blankets, beds, heaters, tents and catering vehicles.
During a visit to Elazig and Malatya, Turkey’s president, Recep Tayyip Erdogan, said that steel-framed houses would be built to provide housing for displaced residents.
“Turkey has begun to heal the wounds of this great disaster in unity, togetherness and coming together,” he said.
Additional reporting by agencies