Officers said they received reports of a one-vehicle crash on the A92 near the Cowdenbeath junction on Saturday evening.
It has since been established a black 4×4 collided with a red Vauxhall Meriva before it left the road at 9.55pm, police said.
John King, 63, from Ballingry was pronounced dead at the scene of the crash, while two boys, aged 12 and one, were taken to the Victoria Hospital in Kirkcaldy for observation.
Inspector Andy Mather, of Fife Road Policing, said: “We have now established that another vehicle collided with the Vauxhall prior to it leaving the road.
“Inquiries are ongoing to confirm the other vehicle involved and identify the driver.
“We are appealing for anyone who may have been travelling in the Cowdenbeath and Lochgelly area or on the A92 dual carriageway around 9pm to 10pm that evening, particularly if you saw a black-coloured 4×4-type vehicle.”
He added: “Anyone who may have dashcam footage from the time is asked to review this and pass on anything which may be of note.
“Any information can be passed to police by calling 101, quoting incident 3941 of 12 September or by contacting Crimestoppers on 0800 555 111.”
Mr King’s relatives said: “The family are devastated by the sudden death of John.
“We would like to thank everyone for their thoughts and condolences.
“We would ask for privacy at this sad time.”
Emergency services said they were called to the area on Saturday at about 9:55pm. The road remained closed until 1pm on Sunday.