Three people got out of a dark-coloured sedan but it was not clear how many opened fire at the house in Ambarvale in Sydney's southwest outskirts on Monday, police said.
There was a second public shooting little more than a day later, when bullets were fired at a house in Guildford West in Sydney's west about 2am on Wednesday.
There is no suggestion the incidents are linked and no injuries were reported in the second shooting.
Police are investigating if a burnt-out car found in nearby Villawood a short time after Wednesday's shooting is linked to the Guildford incident.
Fire crews were called to the blaze about 2.50am but the vehicle was destroyed.
It followed emergency services being called to a Dickens Road property about 11pm on Monday to treat Kim Duncan, 65, before she died at the scene.
The home was riddled with bullet holes.
The attack was targeted but it was unclear if Ms Duncan, who was inside the house, was the intended victim, police said.
A 21-year-old woman and a 34-year-old man inside the home were not injured.
The occupants of the house, who authorities believed had lived there for six to eight weeks, were known to police.
Police were unable to interview some distraught family members and said they would give them more time to process the death.
"It's tragic ... your mother and the grandmother to your children has been shot by cowards that stood out the front of the house," Detective Superintendent Grant Healey said.
Police continue to search for the three people seen getting out of the car.
Nearby resident Louise Hoser said she heard gunshots soon after 10.30pm.
"Within 20 minutes I went to bed and my bedroom just lit up with the police lights ... they didn't have the sirens going, but there was a lot of police presence and ambulances up there," she told AAP.
"I woke my house up to alert them that something was happening ... it was very distressing to hear the family, and shocking to find out she was an elderly lady."
Bullet holes could be seen near stairs leading to the front of the home and on the front wall of the house.
Evidence markers dotted the driveway at the home on Tuesday as officers and the homicide squad began their probe.
Police said members of the public would be key to their investigation and asked witnesses to contact Crime Stoppers.
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