The rescued girl was immediately taken by the PRC Emergency Medical Services (EMS) team to the Doctors Community Hospital in the Mawab municipality of Davao de Oro.
The PRC also took the two-month-old boy, reportedly suffering from severe diarrhea, to the same hospital.
The number of people killed in the landslide has increased to 35 with hopes of more survivors diminishing, Reuters reported, citing officials.
More than 75 people remain missing and 32 are reportedly injured.
The landslide struck the gold mine in Maco town in the province of Davao de Oro on Tuesday night, burying homes and vehicles transporting people, including two buses with dozens of miners.
“It happened so fast. They suddenly saw the landslide cascading directly towards them,” government spokesperson Edward Macapili said.
The three-year-old girl was saved from the rubble as rescuers used their hands and shovels to find survivors, Mr Macapili told AFP.
Photos shared by PRC show rescue workers carrying the girl, wrapped in an emergency blanket and connected to an oxygen tank, to the nearby hospital in Mawab.
“It’s a miracle,” he said, adding that saving the child “gives hope to the rescuers.”
“We can see in the social media posts that the child did not have any visible injuries,” Mr Macapili added.
Even though over 300 people were involved in rescue operations, the process was being hampered by thick mud, heavy rain, damaged communication lines, and the threat of further landslides, officials said.
Rains have led to tens of thousands of residents moving to emergency shelters.
Heavy rainfall, mountainous terrain, and deforestation from mining have made the islands prone to landslides.
Earthquakes also stopped the search for more survivors on Saturday.
A 5.6 magnitude quake struck Mindanao in the Philippines, but no damage is expected, according to the Philippine seismology agency.