Advances in DNA technology and tip-offs have provided vital clues, with police now appealing to the woman's neighbours and anyone else with information about the assailant to help finally solve the brutal crimes after more than four decades.
A man armed with a knife first forced his way into Jessie Grace Lauder's Newport home in Melbourne's west on September 22, 1981 and confronted the 82-year-old woman as she was in bed.
He then took her into another room and sexually assaulted her before rifling through her purse for money and making his escape over her back fence.
Less than two years later, Ms Lauder was again attacked in her own home.
On July 6, 1983 a man forced his way into her house as she was in her lounge room getting ready for bed.
Police believe he then led her into the kitchen to check no one else was home before taking her back into the lounge room and sexually assaulting her.
The man referenced the earlier assault and told Ms Lauder not to call police.
The widow lived alone at the time and had been in the same home for 55 years. She died in 1993.
The offender was described as being aged between 20 and 30 with dark hair, a fair complexion, about 175 centimetres tall and having an Australian accent.
It's believed he was wearing gloves, a beanie and work boots and had concealed his face.
Police believe people who lived nearby at the time would have known the offender and have urged anyone who may have witnessed or heard anything about the attack to come forward.
Ms Lauder lived on Mason St in Newport and investigators are particularly keen to hear from anyone who remembers a man matching the offender's description who may have lived on that street or surrounding roads including Johnston St, Oxford St, Lucius Lane and Cunningham Lane.
A $500,000 reward for information announced in 2016 remains on offer, or the option of indemnification from prosecution.
Detective Inspector Mark Burnett said new information provided so long after the attack can still make an enormous difference.
"Though Jessie is sadly no longer alive, these brutal attacks have had enduring effects on her family," he said.
"Jessie was a vulnerable older woman who should have been safe in her own home.
"On the other hand, this man has lived these last 40 years with relative freedom and no repercussions yet for what he did.
"It is as important as ever that the person responsible is brought to justice and I absolutely believe that with the right information, it can be solved."
