Police said the body was found after reports of a domestic argument at a premises in Boberrit Wynd, Sydenham, about 10.40pm.
They believe a woman from the house went to a nearby sports ground oval at Overtonlea Boulevard and was followed from the house by a man.
An argument took place on the football oval and the man collapsed and died with a stab wound to the upper body, police said.
A person who heard the woman calling out went to her assistance and police were called.
The dead man is believed to be in his 40s.
The woman is aged in her 20s.
Police have set up a crime scene at the house and at the oval and forensic specialists have examined the scene.