Police say he threatened her with a large stick and demanded she hand over cash at Melbourne’s East Geelong Cemetery.
She gave him money but when a Good Samaritan stepped in to help her, the teenager fled.
Police are now appealing for the the female passerby to come forward as they hunt for the perpetrator.
Senior Sergeant Mark Guthrie told the Geelong Advertiser: "When the young male has seen this lady who intervened he has run away.
"We are hoping she can come forward and assist police."
While unhurt, the pensioner was left shaken by the terrifying ordeal.
He added: "What sort of world have we come to when a woman can’t even grieve at her deceased husband’s grave."
The offender is said to be Caucasian, about 14-15 years old and dishevelled in appearance.
Anyone with information is urged to contact Crime Stoppers on 1800 333 000 or Geelong CIU on 5225 3100.