The blaze broke out in the living room of the three-storey tenement in Neilston Road yesterday at 12.45pm after a couch ignited.
Residents, who were alerted by smoke alarms, called 999 and firefighters rushed to the scene.
When they arrived the woman was being helped from the building by people who were passing by stopped to help.
The woman was taken to the Royal Alexandra Hospital for a precautionary check-up.
Watch manager at Paisley fire station, Niall Macleod, said: "Cigarettes must always be properly put out and anyone who is tired or feeling drowsy should avoid smoking if they are sitting or lying down."
He added: "It's all too easy for someone to fall asleep and start a potentially devastating fire."