The flames got bigger when they caught onto sponge-based furniture in the hall, emitting thick toxic fumes in the ground floor apartment of a three-story building.
The brothers were aged six and 10, while the third victim, whose relation to the other two has yet to be ascertained, was 28.
Ali Al-Ghamdi, Makkah Red Crescent spokesman, confirmed that two Red Crescent teams were sent to the accident site, where they found three bodies.
Civil Defense teams rescued six people from the building. None of them was seriously injured.
Sarhan said an investigation into the cause of the accident is under way and and the identity of the third victim is being ascertained.