The 89-year-old answered the door to a man who claimed that he needed access to her home due to an electrical emergency.
It happened on Monday at around 3.30pm at the pensioner's home in Carntyne Road.
She asked the man for identification but he pushed past her, heading for the living room where the opportunist crook snatched a purse from the room and fled.
The raider is white, around 30-years-old, 5ft 3in tall and of medium build, with black hair and dark facial hair.
Constable Mark Nelson, of London Road CID, said: "I'd like to speak to anyone who may have seen this man in the area.
"Elderly or vulnerable people should be on their guard and use door chains when answering callers."
Anyone with information should call 0141 532 4600 or Crimestoppers, anonymously, on 0800 555 111.