Pauline King, described by police as a "reclusive hermit", was found at The Avenues on 22 February.
Alexander Kerry, 23, of Kinghorn Road, Norwich, was sentenced at Ipswich Crown Court after he entered a guilty plea.
He denied a charge of sexual assault and the prosecution chose not to proceed on that count.
Ms King died as a result of a sustained assault with a knife and hammer during a burglary at her home, the court was told.
She lived alone in what police described as a "dilapidated" detached house and neighbours said she was a pleasant but reclusive woman.
Kerry was found later the same day wandering nearby streets covered in blood.
Det Sup Paul Durham described it as a "vile murder" which "sent a shudder of fear" through the community.
Prosecutor Andrew Jackson said Kerry, desperate for money after drinking in a Norwich city centre pub, had broken into the home and beat Ms King to death.
He then tried to set fire to the house to destroy the evidence, he said.
The court heard he was left deeply damaged after his father murdered his mother as he and his brother slept at their home in 2002.
Mr Justice Stuart-Smith said he acted with "animal brutality" to murder Miss King and sexually abuse her dying body in an "act of desecration".
He said: "Nothing begins to explain what you did to Pauline King. She must have suffered terribly."
Kerry had a criminal record including violence and disorderly behaviour dating back to his teens, he said.
Jonathan Goodman, mitigating, said his client had "self-medicated" through alcohol and drugs following the almost "unimaginable" events of his childhood.

The futures of Aston and Coventry stations were discussed by West Midlands Fire and Rescue Authority.
The authority, which said it needed buildings for a "modern-day" fire service, approved its budget earlier.
Plans to demolish Aston's Ettington Road fire station, which was built in 1923, will go before planners.
Phil Hales, deputy chief officer of West Midlands Fire Service, said Aston residents would be consulted as part of the planning process.
The authority says that Coventry's Radford Road station, which was built in 1976, is expensive to run and maintain.
A new station at Aston could cost around Â£7.5m, while the Coventry scheme could cost an estimated Â£6.7m.
English Heritage has said it expected to be consulted on the proposal to demolish Aston fire station if the plan was put forward.
"Aston fire station was listed at Grade II in 2010 and recognised as a carefully-designed building which works well with its surroundings and is a powerful symbol of civic pride," a spokesperson said.
A man who admitted the "vile murder" of an 82-year-old woman in her Norwich home has been jailed for life, with an order to serve 25 years and six months.
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Plans to demolish and replace two West Midlands fire stations - one of which is Grade II listed - have been backed by fire service bosses.