The blaze erupted in the kitchen
The fire broke out in the kitchen of a house at Leckpatrick Gardens, Artigarvan, near Strabane, shortly after midday on Tuesday.
A nearby police patrol went to the scene and found the house well alight.
They discovered the householder, William McAllister, asleep in an upstairs bedroom and led him to safety.
He was treated at the scene for the effects of breathing in smoke.
Sergeant David Burns said a colleague aroused the man.
"He was dazed, confused. He didn't know where he was or why the police were in the bedroom with him," he said.
"We had to lift him from the bed and bring him down. He was still confused.
"I brought him downstairs and he told us he thought maybe his child was still in the house.
"Myself and my colleague went back into the house and went upstairs searching for the child in the bedroom. But there was no child there fortunately."
Mr McAllister's wife, Sharon, said she was grateful their four children, aged between six and 13, were not at home when the blaze broke out.
She said her husband had a lucky escape.
"The police actually saved his life, the fellow from Strabane police station, Mr Burns," she said.
"He saw the shadow on the bed and realised there was somebody in there.
"The bedroom floor was just starting to light when he got out. I think he's a very, very lucky man today."
A senior policeman described the officers' actions as "courageous".
Vandals
The fire is believed to have started accidentally.
Meanwhile, a fire which destroyed a church in Craigavon, County Armagh, is believed to have been started deliberately.
The police say the fire, at the Methodist Church on Drumgore Road, was not sectarian.
The District Superintendent of the Methodist Church in the area, the Reverend Jim Rea, blamed vandals for the fire.