Paul Madin, 37, of Chesterfield, Derbyshire, and son Damien, seven, and three-year-old Dominic were found dead in their blazing car.
The inquest, at Derby Crown Court, was told how Mr Madin set fire to the car, trapping the boys inside. The tragedy, in a lay-by on the A38 near Derby, happened last August just weeks after his 10-year relationship with their mother broke down.
A jury of six women and three men took just 15 minutes to return the verdicts. following a day-long hearing.
The court was told Mr Madin had been depressed in the days before his death and on the day when his estranged partner Alison Makepeace told him there was little chance of their getting back together.
On the afternoon before they died, Mr Madin took his sons to Bakewell. At about 9.20pm he stopped to ask a woman for a light - and then drove off with her lighter.
The alarm was raised minutes later by motorists who saw smoke coming from the car and then realised there was a person on fire getting out of the door. Several passers-by stopped to help, without realising the two boys were inside.
Gordon Deft, of Derby, told the court that he sprayed the burning man with a fire extinguisher, but Mr Madin just returned to the flames.
Home Office pathologist Dr Clive Bouch told the court the two boys died from severe burns but were almost certainly unconscious before the fire took hold. Mr Madin had a non-fatal neck wound but also died from severe burns, he said.Reuse content