Police said they believed it was a targeted attack and part of an ongoing feud in the north of the city.
It took place at the victim's flat in Liddesdale Road, Milton, at about 13:40 on Saturday.
The man was taken by ambulance to hospital in Glasgow, where his condition was described as stable.
Police are treating the incident as an attempted murder.
Police said two men were seen leaving the flat after the attack before getting into black Audi estate car in Scalpay Street and driving away at speed.
A short time later, a black Audi was found burnt out in the grounds of Lambhill Cemetery on Tresta Road.
The suspects were described as being of average height and build, wearing dark clothing and masks.
Det Ch Supt Kenny Graham said: "We need people to come forward with information about either the attack itself or who maybe saw the car being set alight or going in to the cemetery.
"We also have still to establish if there was a third person in the car or whether the two men got in and drove off.
"Police are checking CCTV and speaking to people in the area to get as much information about this as possible and to catch the people responsible."
He added: "Whilst we believe that this was a targeted attack and part of an ongoing feud in the north of the city, for men to be running about with knives, driving at speed along busy roads and burning a car in broad daylight in a busy residential area is contemptible with no regard for others that could have become involved or hurt.
"We are particularly keen to hear from drivers who were in the area and who may have any 'dashcam' footage of the two men or the Audi."
A 41-year-old man has been seriously injured after being attacked at his home in Glasgow by two masked men armed with knives.