Firefighters were called to the scene in Westmuir Street in Glasgow's East End after a fire broke out in the block.
Crews from Calton and Springburn Community Fire Station were were called to the fire drama in the Parkhead area.
The blaze broke out around 2am on Saturday.
Six firefighters wearing breathing apparatus entered the building.
The fire officers searched the first, second and third floors of the building, and rescued a woman and a boy from their home.
Both the woman and child were suffering from smoke inhalation and firefighters treated them on the scene while waiting for an ambulance.
The baby was then taken to the city's Yorkhill Children's Hospital for a precautionary check-up.
A spokesman for Strathclyde Fire & Rescue said: "A fire in the communal area of a block of flats is obviously extremely serious, as it could potentially compromise residents' ability to escape from the building.
"In this instance firefighters were on the scene within minutes and successfully extinguished the flames, but smoke is every bit as much of a threat to life as flames.
"Crews provided oxygen therapy to a woman and child suffering from slight smoke inhalation, and our colleagues from the ambulance service decided the child should be checked-over in hospital.
"This incident should remind everyone of the need for every home to have a working smoke alarm.
"Fire can strike anywhere and having a working smoke alarm is often the difference between life and death."
The fire service provides free Home Fire Safety Visits to residents.
To arrange a free Home Fire Safety Visit for you or someone you know – such as an elderly or vulnerable relative, friend or neighbour – call Strathclyde Fire & Rescue on 0800 0731 999 or text "check" to 61611.