Martin Dukagjini was only arrested in 2019 through the "tenacity of the investigators" and advances in DNA analysis, said Justice Des Fagan.
Three drops of his blood were found to be on the pyjama pants of Tatiana Sokoloff, a lecturer in Italian at the University of Sydney.
After a judge-alone trial in November, Justice Fagan found the now 65-year-old guilty of murdering Ms Sokoloff at her Haberfield home on September 4, 1986.
In the NSW Supreme Court on Thursday, he jailed him for 20 years with a non-parole period of 13 years.
The 56-year-old lecturer had lived with and cared for her 87-year-old mother, Klaudia, who was frail and deaf.
The judge found Dukagjini broke into the home to steal from it, before being disturbed by Ms Sokoloff in a sunroom at the rear of the house.
Acting in panic, the unarmed intruder killed her with objects to hand.
He strangled her with an electrical cord and bludgeoned her with a piece of timber as she lay on the floor.
Police failed to identify a perpetrator despite extensive inquiries among tradesmen, neighbours, colleagues and students, and business people including those from whom she bought antiques and jewellery.
Blood swabs and other forensic items from the scene were retained but DNA testing and comparison was not yet available in 1986.
But the judge found subsequent testing revealed three drops of Dukagjini's blood on the front of the pyjama pants worn by Ms Sokoloff when she was killed.
A drop of his blood also was found on the patio.
Further, male DNA in a small bloodstain on the piece of timber was consistent with having come from Dukagjini.
He was a "habitual house-breaker at the time of the murder" and lived three kilometres from the scene.
"He was present in the house on the night in question, for the purpose of stealing, and he ransacked the place in search of valuables, wearing gloves," the judge found.
Dukagjini, who continues to deny the murder, had a long record for house-breaking in the 1980s for which he was jailed in the 1990s.
The judge noted his offending involved no other crime involving violence.
Ms Sokoloff's mother has long since died, but the judge said the court could readily infer the impact on her of discovering her daughter's body in the middle of the night.
She then briefly resided in a home for elderly people of Russian descent, before a friend of her daughter's and his wife invited her to live with them and their children.
Dukagjini left his birthplace of Albania in about 1976, coming to Western Australia at the age of 24 without any job skills.
There he began his career of house-breaking, which continued when he moved to NSW until his incarceration and subsequent move to Victoria.
The judge found he did not pose a significant risk of re-offending, certainly not violence matters, but was not remorseful.
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