Paramedics and London's Air Ambulance rushed to the address on Chestnut Avenue but the victim died at the scene.
The number of killings in the capital this year has risen to 60 after an 18-year-old man was discovered with serious injuries in Forest Gate, east London, on last night.
In relation to the Brixton incident, police arrested a man in his 20s on suspicion of murder.
Two people have been stabbed to death in the capital within minutes of each other in separate domestic incidents.
On the same evening, Amaan Shakoor, 16, became the youngest murder victim of the year so far when he was shot in an attack in Walthamstow.More news: Meghan Markle and Prince Harry Name Alexi Lubormirski as Royal Wedding Photographer
The brutal attack comes just hours after a 17-year-old boy was stabbed several times in Limehouse. When they arrived to the scene, they found the victim, Christopher Miles, dead.
In the first stabbing, which took place on Friday afternoon around 3:20pm, three male suspects between 20 and 25 years old chased a 26-year-old man into a building on the 2100 block of Mission Street.
Rockford Police say officers responded to the stabbing around 6:30. He is in custody at a south London police station.
Police said his family were still being informed and that formal identification and a post-mortem would be arranged.