Sandra Weir, 41, battered pensioner Mary Logie to death in her home in Leven in January.
The pensioner suffered multiple head wounds, possibly inflicted by a heavy rolling pin.
Police said Weir was "a callous and uncaring individual who regularly exploited Mary Logie for financial gain".
Weir had been stealing money from Mrs Logie to fund her drug habit.
At the High Court in Edinburgh, Weir had lodged a special defence of alibi claiming that around the time of the murder she was elsewhere in Leven.
She was convicted following a 10-day trial. She will be sentenced in January at the same court.
Judge Michael O'Grady said: "In these courts we do not weigh the worth of victims; nor should we. All life is precious.
"But, on the evidence before me, Rae Logie was a decent, kind, tolerant and harmless elderly woman. That you should have betrayed her trust is shocking enough."
He said Mrs Logie's death was "breathtakingly wicked".
"I have no doubt then you left her for dead and went about your business. Instead, you found she was still alive and that you could not allow," he added.
"And so, as she lay defenceless, you simply finished her off."
The court heard Ms Logie was found dead in her home in Green Gates on Tuesday 5 January.
The pensioner had 31 injuries to her head and neck, and died as a result of "blunt force trauma" to her head.
The court heard that Weir had become close to Mrs Logie and had acted as her unofficial carer.
It emerged she had been a drug addict since her 20s and had racked up debts.
Det Ch Insp Keith Hardie, of Police Scotland, said: "Sandra Weir is a callous and uncaring individual who regularly exploited Mary Logie for financial gain.
"She would use coercion to obtain cash and other items of value from Mary before ultimately subjecting her to a horrific attack, which left the 82-year-old with fatal injuries.
"The level of violence inflicted upon Mary, coupled with the prolonged period of bullying and intimidation, demonstrated Weir's complete disregard for the wellbeing of her victim."
The officer added: "Mary's death had a profound impact on the local community and we are extremely grateful to the local residents who came forward with vital information that allowed us to identify Weir and bring her to justice."
Earlier Alex Prentice, prosecuting, had told the jury there was evidence that Mrs Logie was still alive after being attacked in the morning.
He added: "I suggest that evidence will cause you to conclude that she was conscious but lying there.
"Mary Logie remained alive. The wounds incapacitated her and she remained there that day."
He said evidence given by the accused and a witness indicated that Mrs Logie was attacked for a second time later in the evening.
Analysis of the spot where Mrs Logie's body was found revealed both "fresh blood" and "clotted" blood, suggesting there were two attacks against her.
The lawyer said Weir had probably administered the blows which killed Mrs Logie on the evening of 5 January.
Mrs Logie, who was born and brought up in Methil, worked in a local chemist after leaving school and before meeting her husband Walter.
She was married for 33 years and the couple had two sons and a daughter.
Mrs Logie later worked as a part-time cleaner at a local photography business and as a home help, and was involved with the Church of Scotland Guild.
The pensioner, a regular churchgoer, had planned to visit a friend in hospital that day but did not turn up.
She had spent Christmas with one of her sons in England not long before her death and was said to have led an active life, with lots of friends.
A heroin addict has been found guilty of the "horrific" murder of her 82-year-old neighbour in Fife.