Officers found the body of a 26-year-old-man in a flat on Drive Road, Govan, after they were called to a disturbance at 2am on Friday.
As reported in later editions of last night's Evening Times, the street was cordoned off as police interviewed residents, motorists and passers-by.
Forensic officers, wearing protective white coveralls, entered the tenement flat where the body was found, which overlooks the children's play area at Elder Park. A mobile incident unit was set up in the street.
Police say they are following a "positive line of enquiry."
Residents woke up from celebrating the January 2 bank holiday to realise their street was cordoned off, with access to and from the park restricted. Only those staying in the street were allowed to come and go.
One local man, who did not want to be named, said: "They don't shut down a whole street for nothing."
A local shopkeeper said: "Customers have been saying the police have been there almost all night. This is Govan, though, so you do expect this.".
A Police Scotland spokeswoman said: "At around 2am on Friday officers were called to a report of a disturbance at a flat in Drive Road, Govan. As a result a 26-year-old man has died. A post mortem examination will be carried out in due course. Police are treating the death as murder."