Firefighters pulled the trio from an upstairs back bedroom of the three-storey home on Hill Top Mount in Chapeltown.
West Yorkshire Fire and Rescue Service said all three were "conscious and breathing" as they were taken to hospital by paramedics.
After ringing 999 at just after 1.25am on Wednesday, the mother was given survival guidance before fire crews arrived.
A spokesman for the fire service said: "It was a matter of keeping them calm. We got her to close all the doors to reduce the smoke and made sure we knew where she was and that everyone in the house was with her."
The blaze involved 75% of the house, the fire service said, and was ongoing at 2.15am.
It is not yet known where the blaze started, or what caused it, but a fire investigator is at the scene.