The doctor dismissed the concerns of Joseph Seevaraj's frantic parents and told them to wait for antibiotics prescribed two days previously to take effect. Hours later the three-year-old was dead.
The inquest was told that if he had been taken to hospital, as his father had suggested, he would still be alive.
The errors in Joseph's treatment were described by Brighton and Hove Coroner Veronica Hamilton-Deeley as 'total and complete'.
'He needed basic medical attention,' she said. 'The failure to provide it was gross failure.'
She said she was satisfied that there was a clear connection between this failure and his death.
Joseph, who lived with his parents, Nicola and Jean, in Hove, fell ill with tonsillitis on January 18.
He was prescribed antibiotics at Royal Sussex County Hospital in Brighton, but his condition worsened two days later with the onset of vomiting and diarrhoea.
His parents telephoned the privately-run out-of-hours Brightdoc service at 11pm on January 20 and spoke to Dr Tilo Schippers.
His father, Jean, told the doctor that he was concerned his son was dehydrated and was unable to retain the drugs because of the sickness he was suffering, and asked if he should take his son back to hospital.
But Dr Schippers - who has since quit the Brightdoc service - insisted that there was no need to panic.
Joseph's parents checked on him throughout the night but at 7am they found him dead.
The coroner recorded a verdict of death from natural causes but said neglect had contributed to his death.
Mr and Mrs Seevaraj declined to comment after the hearing but are understood to be considering legal action.
John Vezey, clinical governance manager of South East Health Ltd, which runs Brightdoc, said Dr Schippers had left the service.
He added: 'We have done all we can to learn from this terrible tragedy.'
Before April 2004, GPs provided out-of-hours patient care between 6.30pm and 8am on weekdays and 24 hours a day at weekends and on Bank Holidays.
But out-of-hours services are now provided by a range of organisations, including private firms.
A study by MPs last year found only one in 50 out-of-hours services was meeting targets set to ensure patients get the proper treatment, reports Daily Mail.