Kenneth McNeill, 52, was found dead in a third-floor flat on Dumbarton Road in Scotstoun, Glasgow, at around 1am on Thursday.
Detectives said the victim was the "intended target" of the attack.
Paramedics were called but Mr McNeill died at the scene.
The suspect is described as a white man, 5ft 6in or 5ft 7in, medium to skinny build with short fair hair.
He was wearing a light-coloured top. His age is not specified.
Area Commander Chief Inspector Mark Sutherland said: "I would like to reassure members of the public, particularly those who live in the area of the flats, that everything is being done to trace the person responsible.
"I am aware that local residents will be shocked and alarmed by this incident, however extra patrols will be in the area.
"I would urge anyone who has concerns to speak to the officers."