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Their Bay View Rd flat caught fire about 11.45pm on Saturday, and given the speed at which the blaze ripped through the house, they were lucky they were awake at the time, firefighters said.
Tenant David Tait (19) said he had been sitting in his lounge playing Xbox Live against a friend living in nearby Tedder St and left the house briefly to pick something up in Tedder St.
Mr Tait said he left the game's microphone on so his partner could call to him and his friend if she needed anything.
His 18-year-old partner was having a relaxing night in bed with a cup of tea and some candles.
She left the room to refill her teapot and returned to find her pillow on fire.
''She grabbed the pillow and chucked it into the sink in the bathroom. There was a couple of embers left on the bed.
''She came back [to the bedroom] and the whole bed was alight. It just spread from there.''
Mr Tait said his friend heard her say ''there's a fire'' on the microphone, so he raced home and found smoke billowing from the flat.
His partner had attempted to use a garden hose to put out the fire but it was not connected, he said.
Mr Tait said by that stage it was too late and he took his partner and daughter outside to safety.
''My only thought was to go for it - get everyone out.
''It went up in flames - two minutes and it was spread everywhere,'' he said.
A neighbour called the fire brigade.
Mr Tait said he tried to go back inside to retrieve some valuables, but the fire had spread so quickly it was impossible to re-enter.
''We're in shock. We've just lost everything.
''It's still sinking in.''
The couple had no insurance, he said.
''As 18- and 19-year-olds, you don't think of insurance. You should think of smoke alarms, but we just didn't check.''
Mr Tait said he and his family were grateful for the support they received from friends and extended family.
''We're staying with my mum at the moment. It's been overwhelming how much help we've had.
''There's been people that we don't even know helping us out, and it's crazy how many messages of support we are getting.''
He said one of the most frightening things about the experience was there was a smoke alarm in the house, but it did not sound.
''We never heard it beep or anything. It didn't go off.''
He urged people to learn from their experience and check their smoke alarms, and electrical cords, power points or anything that could cause a fire.