The 52-year-old man died after he was attacked in a third-floor flat in the tenement block in Dumbarton Road, Scotstoun.
Detectives from the Specialist Crime Division, said the victim was visiting the homeowner, when the intruder burst in and killed him.
The alarm was raised shortly before 1am today when officers were called to reports of a disturbance.
Despite efforts from paramedics, the 52-year-old died at the scene.
Detective Chief Inspector Jim Smith, from the Major Investigation Team, is leading the investigation.
The senior investigating officer said: “Our inquiries are at a very early stage to establish the circumstances which led to the death of this man.
“Although a post mortem examination will be carried out, we are treating his death as murder.
“At this time, it is believed that a man arrived at the flat around 12.50am, forced his way into the house and assaulted the victim who was not the householder.
“It is not clear what the motive was but it was not a random act. It would appear that the victim was the intended target.
“However at this time it is unclear why.”
Witnesses, or anyone who heard a disturbance at the flats, have been urged to come forward and contact police.
Police said the suspect is a white male, around 5ft 6in, of medium to skinny build with short fair hair.
He was wearing a light coloured top.
Area Commander, Chief Inspector Mark Sutherland, said “everything is being done” to find the killer.
He said: “I am aware that local residents will be shocked and alarmed by this incident.
“However, extra patrols will be in the area, and I would urge anyone who has concerns to speak to the officers.”
Anyone with any information is asked to phone 101.