It began after three men entered the flat in Headfield View, Thornhill Lees, at around 6.30pm.
One of the men was carrying a knife and stabbed the victim, causing two wounds in his back.
The suspects also damaged a car outside the property as they fled the scene.
Police said the trio had driven off in a black Range Rover and a black hatchback.
A spokesman said: "The 30-year-old male victim was taken to hospital where he remains in stable condition.
"His injuries are not thought to be life-threatening."
The first suspect is described as Asian, aged 20, 5ft 7in and of medium build, with short black hair, stubble beard and moustache. He was wearing jeans and a grey jumper.
The second is Asian, aged 20 or 21 years old, 5ft 6in and of medium build, with a thin line on his face and a small moustache. He was wearing light blue jeans and a red jumper.
The third suspect was an Asian male, aged between 23 and 24 years old, 5ft 6in and of a small build, with short black hair, a thin moustache and a stubble beard. He was wearing a light grey tracksuit.
Anyone with any information about this incident, who saw the vehicles in and around the area or who recognises anyone matching the descriptions is asked to contact the police via 101, quoting crime reference 13180048158.
Information can also be passed anonymously to Crimestoppers on 0800 555 111.