They are managing to send them supplies of water, glucose and oxygen through small gaps in the debris.
Tapping sounds have been heard from inside the building in the city’s busy Kariakoo market area.
Five people are known to have died, while 77 have so far been brought out alive.
Large crowds of bystanders applauded as rescue teams ferried survivors on stretchers past huge piles of concrete debris to take them to hospital.
Seven people were rescued on Sunday from the building’s basement, Dar es Salaam’s regional commissioner Albert Chalamila told The Citizen newspaper.
“We are hopeful that more survivors will be found,” he said.
It is not clear how many people remain trapped.
Prime Minister Kassim Majaliwa said the authorities “won’t rest until we have made sure we have been able to rescue each and every person or soul who is trapped in the rubble”.
After the building first gave way at about 09:00 local time (06:00 GMT) on Saturday morning, hundreds of first responders used sledgehammers and their bare hands to pull away the debris, reports the AFP news agency.
Cranes and other heavy machinery were later brought in to help.
Fortunately, the building came down before the market area had become too busy.
Authorities are yet to determine the cause of the collapse, but investigations are expected to begin once rescue efforts are complete.
Dar es Salaam is one of the world’s fastest-growing cities and reports say that building regulations are not always enforced.
