The impact pushed the house out of alignment.
Mr Howard was horrified to see that the vehicle had passed within 1m his of 7-year-old daughter's bedroom.
Constable Scott Crook of Greymouth police said if the car had hit the bedroom it probably would have killed the sleeping child.
"We were very lucky this did not happen during the day - the children may have been playing in the yard, and the debris from the fence would have been missiles flying through the air."
Pieces of the fence were found on the roof of the house.
Police were on the scene within two minutes of the call and while a sniffer dog quickly got the scent of the driver, lost it nearby.
"We believe the driver sustained some sort of head injury and want to hear from anyone who may have information about the crash," Mr Crook said.
He hoped that "someone with a conscience" would come forward.
"A child could have been killed."
Police believed both speed and alcohol contributed to the crash.