Annie Besala Ekofo, 53, and Bervil Kalikaka-Ekofo, 21, were found dead in East Finchley on Thursday.
The Met Police said a 24-year-old man was arrested on Sunday on suspicion of murder and is in custody at a north London police station.
A 20-year-old man held on Saturday has been released on bail until October.
Scotland Yard also revealed Mr Kalikaka-Ekofo had died from a gunshot wound to the head.
A post-mortem examination for the University of West London psychology student took place at Northwick Park Hospital mortuary on Saturday, it said.
A post-mortem examination on Ms Besala is yet to take place.
Detectives earlier launched a fresh appeal for witnesses.
They said there was no evidence to suggest the pair were the intended victims but would be exploring whether anyone else linked to their address could have been a potential target.
Police were called to Elmshurst Crescent by the London Ambulance Service at about 06:25 BST and found the pair in their flat.
Four other people, including a child, were also at the property at the time of the incident but were not harmed.