Investigators believe Cali, 53, was inside his Todt Hill house with his family Wednesday night when the person or people responsible rammed the mob boss' vehicle with a blue pickup truck, prompting him to come outside, sources said.
No arrests have been made. He died in prison in 2002.
According to the New York Daily News, a family member of Cali's called 911, telling a dispatcher that the gunman's getaway vehicle ran him over.
United States media reported that his death marked the first murder of a NY mob boss in 34 years, since the death of Paul Castellano - another Gambino family boss - by order of John Gotti.
DeCicco was the No. 2 figure in the Gambino family in 1986 when he died in a auto bombing in Brooklyn.
Later, in November 2008, Weinstein lowered the prison term to 16 months after prosecutors recalculated the victim's loss as $8,000, not $13,000.
Paul Castellano also owned a home there.
But Gravano would eventually testify against Gotti, leading to Gotti's 1992 conviction in five murders - one of several major convictions that thinned the Mafia ranks in the 1980s and '90s.
Meanwhile, on March 13, two heads of the Bonanno family, Joseph Cammarano Jr. and John Zancocchio, were acquitted in court on conspiracy and racketeering charges, the New York Times reported.
Cali's demeanor, while he was alive, was completely unlike the manner John Gotti conducted himself, the latter an extravagant and ostentatious mobster the Mob hadn't seen since the days of Al Capone. An Italian mobster said Cali was "everything over there" in NY and referred to him as "a friend of ours".
Witnesses told local media of hearing at least six shots coming from outside, and seeing Cali's family members rushing outside and crying next to his body.
Last week, Carmine Persico, the 85-year-old former boss of the Colombo organisation, died after serving 33 years of a 139-year prison sentence.
It is unclear who killed Cali, who reportedly became the head of the crime organization in 2015.
"Papa! Papa!" one man cried before laying down on the grass, sobbing, the witness recounted.