A high-speed chase through the Cape Flats ended in a gunfight after a car rammed pursuing traffic co.
A businessman, who asked not to be named, told the newspaper that Pistorius had arrived uninvited at a party that the businessman was hosting in Illovo, Johannesburg, on April 6 last year.
Pistorius is currently on trial, charged with murdering his girlfriend, Reeva Steenkamp, whom he shot dead through a locked toilet door at his Pretoria home on Valentine's Day last year. Pistorius has claimed that he shot Steenkamp by mistake after believing there was an intruder in his house.
On Sunday, the newspaper quoted unnamed sources, reportedly guests at the party in April, who said that, at the event, Pistorius had appeared subdued at first, but after drinking heavily, had taken to the dance floor as well as tried to flirt with a woman - who rejected him.
Recently, reports emerged that Pistorius had been involved in an altercation with businessman Jared Mortimer at an upmarket club, the VIP Room, in Sandton, Johannesburg, last Saturday night.
Mortimer told The Star newspaper that Pistorius had been intoxicated at the time and had insulted President Jacob Zuma.
Subsequently, Pistorius's uncle, Leo Pistorius, released a statement, on behalf of the family, in which he said that the athlete's move to venture into a public space while the trial was under way had been unwise.
He said the family had witnessed Pistorius's "escalating sense of loneliness and alienation. This, we believe, is underlying some of his self-harming behaviour."
Leo Pistorius also refuted Mortimer's version of events, saying the businessman had been the "aggressor" in the incident and was "peddling untruths".
Pistorius's murder trial is set to resume on August 7, when final arguments are expected to be heard.