Fire crews were called to the blaze in Peter Street, Blackpool, just before 12.45am today after the alarm was raised by a neighbour.
When they arrived, flames were spreading through the ground floor hallway which is the entrance to two flats.
Smoke alarms had gone off and a man and woman living in the ground floor flat attempted to put the flames out themselves.
The man was treated for burns to his feet and the woman was treated for smoke inhalation by the fire brigade.
M6, M61 and M55 delays in Preston due to Blackpool Air Show and Lake District holiday traffic
Lanes reopen after car crash on M6 brings Preston motorway traffic to a halt with severe delays expected
Driver caught 'snoring merrily away' on the M6 near Bamber Bridge with full-beam headlights and engine running
Thunderstorms and heavy downpours of rain predicted to hit Lancashire as Met Office issues yellow weather warning
Two Preston men arrested after serious assault near Harris Museum
A woman and baby from the first floor flat escaped outside before fire crews arrived.
Firefighters wearing breathing apparatus went into the building to fight the flames.
Severe damage was caused to a carpet on the first floor, with smoke damage to the ground floor common entrance hallway and to the ground floor and first floor flat common areas.
A joint investigation into the cause, which is believed to be suspicious, has been launched by the police and fire brigade.
Firefighters also warned people not to attempt to put out fires themselves, and to ensure their alarms are working.
Warren Topp, watch manager at Blackpool Fire Station, said: “The fire service always advise occupants to ‘get out, stay out and call the fire service out’ ensuring the door is closed on a fire and all occupants are evacuated.
“No attempts should be made to extinguish a fire that has the potential to endanger life.
“The smoke from the fire has the potential to overcome persons and render them unconscious.”
To get your alarms fitted or checked go to www.lancsfirerescue.org.uk or call free on 0800169 11 25.