The young man was later seen speaking to police outside, visibly distressed and with blood on his clothes.
The 28-year-old alleged intruder, Xochil O’Neill from Heidelberg West, suffered critical injuries during the struggle and was rushed to Royal Melbourne Hospital under police guard. His condition was improved to serious by Thursday morning.
Police are investigating whether Mr O’Neill is the same man neighbours say they saw acting erratically, climbing trees and hiding under cars in the street not long before the fatal attack.
One neighbour said they believed Mr O’Neill was living in a house directly across the road from the victim.
Mr O’Neill is expected to be in custody for some time, police said.
“The exact circumstances surrounding the incident and the man’s motive for attending the property are still being determined,” the police spokeswoman said.
The 61-year-old woman, who neighbours said lived with her two adult sons and was described as a “very nice, lovely person”, died at the scene.
One nearby resident said he was outside having a cigarette when he heard a woman shouting.
“I heard her yelling, ‘get out of the house now’,” he said.
“Then just quiet after that, didn’t hear anything. Then later the sirens. They came quick as anything, I’ll give them that.”
A police spokeswoman said: “It is believed a man broke into a house before assaulting a female occupant inside.”
Homicide detectives are not looking for anyone else over the woman’s death. They remained at the property on Wednesday as crime scene investigators carried bags of evidence outside.
About 8.30am on Wednesday, two women and a man arrived at the scene and were visibly upset as they spoke to police, before driving away again. The street was reopened at 4.45pm.
In an unrelated incident, a woman was charged with the alleged murder of a man stabbed in Heidelberg West last week. The 55-year-old man was found dead at a home at Koitaki Court about 12.05am on Friday.
Anyone who witnessed the incident or who has information is urged to contact Crime Stoppers on 1800 333 000 or submit a confidential crime report at www.crimestoppersvic.com.au.
Simone is a crime reporter for The Age. Most recently she covered breaking news for The Age, and before that for The Australian in Melbourne.
Zach is a reporter at The Age. Got a story? Email me at email@example.com