The pensioner was pushed to the ground in Drum Terrace Cemetery, near Easter Road, before the man made off with her handbag, which contained more than 100.
A couple in the cemetery rushed to assist the elderly woman before contacting the police for help.
A spokesman for Lothian and Borders Police said: "This is a disgraceful crime committed against an elderly lady in broad daylight."
The woman was attacked at around 2.20pm on Saturday when she was tending to her daughter's grave in the cemetery, which backs on to the Easter Road stadium.
Clegg says election 'could bring change'
NICK Clegg today claimed the general election could bring "fundamental change" to Britain.
On a visit to Edinburgh, the Liberal Democrat leader said electoral reform was an " absolute precondition" for any post-election deal with the other parties.
And he attacked the current "clapped-out" political system, which he said was "past its sell-by date".
Firefighter in hospital
A FIREFIGHTER was rushed to hospital after a fierce blaze ripped through a warehouse.
The fire, at a unit on the Houstoun Industrial Estate, in Grange Road, Livingston, was so powerful that more than 35 firefighters had to be called out.
The crew member was taken to St John's Hospital after he suffered from heat exhaustion, before being later discharged.
In what was described as a "highly dangerous" situation, firefighters from five vehicles worked quickly to remove four gas cylinders containing explosive material and a large diesel tank from the warehouse, owned by Tone Scaffolding Services.
The fire broke out at about 5:30pm on Saturday.
Stab victim named
A MAN who was brutally stabbed to death by a pair of thugs wearing balaclavas has been named.
Dennis Parker, 27, from Eskside West, Musselburgh, was knifed in the heart in the early hours of Saturday morning after the masked men burst into his flat. His friend, 21, believed to be known locally as "Chalky", was also badly injured in the attack.
It is believed that the row broke out due to a drug debt.
Mr Parker's friend is thought to have stumbled outside to a nearby phone box to call for help shortly after 1am on Saturday.
Both men were rushed to Edinburgh Royal Infirmary for emergency treatment, but Mr Parker, who lived in Musselburgh all his life, later died from his injuries.