Dead are Berricou Subhan, 46, his daughter Sherifa, 14, and five year old son, Musaf.
Subhan's wife Rasheeda Alladin, 33, was also stabbed multiple times, along with the couple's six year old daughter, Lila. The only person to escape injury was seven year old Salin.
The killer has been identified as Sylvan Alladin, a drug addict with a long criminal history.
Police said that at around 9.30 p.m, Alladin went to Subhan's home and began arguing. Alladin pulled a knife and began stabbing Subhan, whose wife tried to intervene. She too was stabbed several times before running to the home of a neighbour.
The killer went into the house and found the four children. Little Musaf was cornered in the bathroom and stabbed to death, before Sherifa was attacked and killed.
When police arrived at the scene, Alladin was still in the house. Corporal Bahadoor and Constable Smith broke down the door and found the man sitting in the house with the two other children sitting on his lap. Their mouths and hands were bound with duct tape. Alladin stabbed Lila on the leg, and police opened fire, killing him, the Express was told.
Rasheeda Alladin is in critical condition at the Intensive Care Unit of the San Fernando General Hospital, where the surviving children are also being treated.
Police said the suspected killer is the son of a butcher. He was also being investigated for several sexual offences.
Corporal Siew is investigating.