Doctors said Dowie Gledhill, aged four months, had a 'nondescript viral infection' and told his parents to take him home.
Twenty-four hours later, he died from septicaemia, caused by the organism also responsible for meningococcal meningitis.
Dowie died on Monday morning at the North Staffordshire Hospital in Stoke-on-Trent.
A second baby, seven-month-old Brett Potts, of Sneyd Green, Stoke-on-Trent, died from the disease in the children's ward at the hospital on Tuesday.
Dowie's parents, Stephen and Janice Gledhill, of Stoke-on-Trent, who married two months ago, said they were considering taking legal action.
Mrs Gledhill, 35, said: 'As far as we are concerned, if the doctors at the hospital had taken better care of our baby he would still be alive today.
'I was panicking because no one would believe what I thought - which was that my baby had meningitis.'
Her husband, also 35, said: 'The hospital is now telling parents to look out for the symptoms of a purple rash. But by the time that rash comes it is too late to save a child.'
The Gledhills took Dowie to the hospital's accident and emergency unit at 8.30am on Sunday. He was examined by a junior houseman, who telephoned a paediatrician where he was told to prescribe Calpol. On returning home, the parents sought a second opinion from an emergency GP who was not told of the hospital's verdict.
Mrs Gledhill said: 'My baby had a temperature of 102F and spots which were growing larger by the minute. The emergency doctor gave the same diagnosis as the hospital. You have got to believe the people in the know.'
Mr Gledhill added: 'We are absolutely devastated that our son has been taken from us, because we think this tragedy could have been avoided. We are in touch with solicitors and looking at the possibility of taking legal action against the hospital concerned.'
Stuart Gray, the hospital's chief executive, said last night: 'This is the subject of a coroner's inquest and we are co-operating fully with the coroner. Until the inquest is over, we are not prepared to make any further comment.'
Meanwhile, doctors investigating the outbreak of the disease, which has left three other children in hospital, said yesterday they believed there was a link between two of the cases.
The announcement came as doctors monitored the condition of a sixth child who is believed to have contracted the disease.
The children had meningococcal septicaemia - blood-poisoning caused by the same bug which is responsible for meningococcal meningitis, which causes swelling in the membranes surrounding the brain which can kill unless it is treated rapidly.Reuse content