Two fire engines from Hartlepool and the ambulance service attended the incident which happened in Sheerness Grove, Hartlepool, on Monday afternoon.
The fire brigade used two breathing apparatus, one hose reel and a positive pressure ventilation fan to help clear the smoke from the property.
They said they were called at around 12.40pm and the incident lasted about an hour.
The casualties were treated at the scene but did not require hospital treatment.
A spokesman for the North East Ambulance Service said: “We were called to reports of a building on fire in Sheerness Grove just before 1pm this afternoon.
"We dispatched two crews from our hazard area response team and treated two people on the scene for smoke inhalation.
"They were discharged on scene without the need for further treatment in hospital.”
The fire brigade said the cause is being investigated as per their usual procedures.