Eileen Blane was thrown to the floor and had her wedding ring taken from her finger in the burglary in Stretford, Greater Manchester, on 3 February.
She spent eight weeks in hospital and died the day after she was discharged.
A Â£50,000 reward is being offered by detectives for information leading to a conviction.
Her son John Blane told the BBC's Crimewatch Roadshow, his mother had answered a knock at the back door, thinking it was the window cleaner.
The suspect pushed into the house and punched Mrs Blane in the face.
During an interview she told police: "He just wouldn't stop hitting me. I just asked him to stop but he wouldn't. He said he wanted gold.. it was just a nightmare."
As she held her hands up to protect herself, the thief pulled her wedding ring from her finger.
While the attacker searched upstairs, Mrs Blane managed to escape and alerted her neighbours, who called the police.
She suffered three cracked ribs, a damaged vertebrae and severe bruising.
Det Ch Insp Richard Eales  said it was a "brutal attack".
He said: "Although Eileen was 87 years of age, she was fit and well and only died as a result of the injuries she sustained on that day.
He urged witnesses to come forward.
The death of an 87-year-old woman who was badly beaten during a burglary is now being treated as a murder investigation, police have said.