Four adults and three children were taken to the Queen Elizabeth University Hospital after a fire began in the close.
Fire crews were called to the three-storey property in Elder Street just after midnight on Saturday.
A spokesman for the Scottish Fire and Rescue Service said: “Firefighters led 15 people to safety following a small fire in the close of a residential building.
“All flats within the three-storey property in Elder Street have been affected by smoke.
“Firefighters extinguished the fire and then swept the premises after the alarm was raised just after midnight.”
The six-strong crew located all the residents who were transferred to the care of ambulance staff.
He added: “The fire service ensured the area was made safe before leaving the scene.”