Sandra Weir, 41, lashed out at pensioner Mary Logie, known as Rae, in her own home in Leven, Fife, in January.
She had also been stealing from the 82-year-old to fund her drug habit.
Rae Logie was a member of Leven Parish Church in Fife and attended three times a week regularly.
Weir had denied the charges, lodging a special defence of alibi saying she was elsewhere at the time.
The trial heard 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 Weir had gotten close to Mrs Logie and acted as her unofficial carer. It emerged, however, she had been a drug addict since her 20s and had racked up debts.
Mary Logie's funeral in February this year
Judge Michael O'Grady told the court: "Rae Logie was a decent, kind, tolerant and harmless elderly woman. That you should have betrayed her trust is shocking enough.
"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.
"And so, as she lay defenceless, you simply finished her off."
Rae Logie's minister and friend, Rev Gilbert Nisbet, said: "The end of the trial regarding the murder of Mary Logie gives an opportunity for the local community and for her family and friends to move forward.
"The evidence given and the reporting of the case in the High Court has reopened the events of last year and brought them back to the forefront of the thinking of many of the people who knew Rae best.
"There is a great deal of sadness that such a thing could happen in this community and people grieve over the circumstances of Rae's death.
"The Christian message of forgiveness is always allied to repentance."
Weir will be sentenced in January next year at the same court.
