She was suffering from smoke inhalation and firefighters provided first aid until the ambulance crew arrived. She was then taken by ambulance to Glasgow Royal Infirmary.
A spokesman for the fire service said: "Incidents like this show how quickly fire can take hold and are a stark reminder of the threat posed to our communities. Firefighters are sadly all too familiar with the tragic consequences of fire, and we are appealing to every member of the public to help us protect their neighbourhood.
"The service has no better ally in the fight against fire than residents of our towns and cities. We need active citizens to take responsibility for their own safety and that of vulnerable people around them, ensuring every home is protected by at least one working smoke alarm."
