The man pounced on the 22-year-old as she was walking home after work along Duke Street in Dennistoun.
He grabbed the woman as she walked near Melbourne Street around 4.25 on Monday morning and tried to drag her down the street.
She managed to break free and ran off east on Duke Street and then made her way home and raised the alarm.
Police said she was able to give them a good description of her attacker.
It is understood the incident is not being linked to the sexual assault of a woman in Glasgow Green last Saturday.
The suspect is described as tanned, in his mid to late 30s, slim to medium build, with short shaved dark hair and a dark neatly trimmed beard.
He spoke with a Glasgow accent and was wearing a green coloured long-sleeved polo top and dark trousers.
Detective Constable Andy Hunter, from London Road CID, said: "This was a very distressing incident for the young woman who had just finished her shift and was heading home for the night.
"Despite this, she has given us a very good description of the man responsible which I am sure someone will recognise.
"As she ran off into Duke Street, she was passed by a black Hackney taxi travelling west towards the city centre.
"Whilst she did not flag the taxi down, it is possible the driver saw her there, maybe not realising she was in distress.
"I am keen to speak to him as he may have information that will help our enquiries."
Anyone with information should contact London Road CID on 101 or Crimestoppers on 0800 555 111.
Investigations are continuing following the sexual assault in Glasgow Green.
The 27-year-old victim was attacked as she walked into the park from Saltmarket at about 11.30pm on Saturday.
She managed to break free and escape.