Georgina Barnett begged Thomas Brogan, 46, to stop as he struck her repeatedly on the head and body in the attack.
Mrs Barnett, who had osteoporosis but led an independent life, was left with multiple bruises and a deep cut to the back of her head. Her injuries included 11 fractured ribs and a fractured sternum. She died five days later in hospital.
Unemployed Brogan pled guilty at the High Court in Edinburgh to murdering Mrs Barnett, who had one daughter, at her home in Ramsay Road, Kirkcaldy, Fife.
The court heard the motive for the attack, which happened on June 25, is unknown. However, in the hours before the assault Brogan appeared to have been angry with a drinking associate "in connection with a mobile phone".
Speaking outside court, Mrs Barnett's nephew Thomas Johnstone, 62, said the death of the much-loved woman had had a big impact on the family.
He said: "She was a very sprightly 90-year-old. She would do everything in the house herself still. We are all still shocked."
Mr Johnstone, who was at his aunt's hospital bedside every night until she died, said: "It's a relief to us we won't have to go through a trial. We hope he gets a just sentence that he really deserves."
Brogan's QC, Mark Stewart, told the court that Brogan apologised for what he did and was "mortified" by his conduct.
But Mr Johnstone said: "An apology doesn't bring my auntie back. That's not good enough."
The court heard that at about 3pm on the day of the attack Brogan spoke to some of Mrs Barnett's neighbours.
He was "extremely drunk and agitated, talking about a problem with his mobile phone and the sim card for it". From what they could tell, his anger appeared to be directed towards a man who was an associate of his, Bryan Hughes.
Later that evening, neighbours heard two dull thuds from Mrs Barnett's living room, then a loud crashing noise before they heard Brogan shouting repeatedly.
They rang police, believing Brogan was fighting with Mr Hughes in the flat, but were shocked to then hear Mrs Barnett's voice saying: "Tam, stop please."
When police arrived, they found Brogan at the flat with his hands covered in blood.
Mrs Barnett, on the floor in the corner of the living room, had severe facial injuries and was bleeding heavily from her head. Blood was spattered on a wall. She was conscious and able to speak to police and paramedics at that stage.
On arrival at Victoria Hospital, Kirkcaldy, she told staff Brogan had beaten her up and that he had been angry. "He was angry with himself," she told them.
The victim later told detectives he had come to her house drunk "looking for the boy next door". She expressed disbelief he would do that to her "just because of that bloody sim card", the court heard.
Her condition worsened and she died on June 30.
Advocate depute Leanne Cross, prosecuting, said: "The scale and nature of the injuries, even allowing for her age, demonstrate a sustained and forcible attack."
Brogan was detained at the scene by police. He told officers: "I done it. I done everything."
The court heard he had 10 previous convictions at summary level, mostly for dishonesty and public order offences.
Brogan will be sentenced on October 30.