Tim Mason, 21, had flu-like symptoms and told doctors he "felt like he was dying" but was discharged just after 8am on March 16 without further treatment, an inquest in Maidstone, Kent, heard.
He was rushed back into Tunbridge Wells Hospital's accident and emergency department hours later for the second time that day where he was appropriately treated and died hours later.
Senior coroner Roger Hatch, delivering a narrative inquest verdict, said that given the results of his blood test, temperature and heart rate, Mr Mason should have received a sepsis screening and been reviewed by a senior doctor.
The coroner said: "Had he been correctly diagnosed it is most likely he would have been prescribed intravenous antibiotics and he would not have died.
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"This should have occurred when he attended the hospital six hours earlier on March 16 when he first presented."
The initial failures to correctly diagnose and treat Mr Mason did not amount to neglect, the coroner said.
The coroner and Mr Mason's family accept that he was appropriately treated when he returned to the hospital.
Maidstone and Tunbridge Wells NHS Trust has accepted liability and admitted breaching a duty of care by discharging Mr Mason with such symptoms.
The coroner also described it as "unfortunate" that Mr Mason did not receive a vaccination.
Staff missed "several" chances to test him for sepsis during the "extremely busy" day despite him displaying signs of the deadly infection, the inquest was told.
The diagnosis was delayed by more than six hours and he would not have died if properly treated, the hearing heard.
The Sussex Downs College student, who was training as an electrical engineer, had also developed the rare but life-threatening W strain of meningitis.
He died after his organs began to fail and he had a cardiac arrest while in an induced coma.
Mr Mason first felt unwell eight days earlier with flu-like symptoms, had taken time off work and college, was seen by a GP but appeared to be recovering.
The court heard how the trust's policy on detecting sepsis at the earliest opportunity was not followed.
Mr Mason's high temperature - at its height more than 39 degrees - and fast heartbeat should have triggered alerts of sepsis and a screening.
His mother Fiona Mason, a personal assistant to the next lord mayor of London Peter Estlin, wept as she told the inquest they first took their son to hospital in the early hours of the morning after he began vomiting "more violently than we have ever seen".
She said he was treated for an "uncontrollably high" temperature but this did not desist.
Mrs Mason had described him as being "frightened" and saying to her and the doctors that "he felt like he was dying".
She told how doctors said he had a virus and the symptoms would get worse before they got better and he could be discharged.
When he came back to the emergency department seven hours later - in so much pain he could not walk or sit up - he was made to wait to be seen, the hearing was told.
When he was assessed again by other doctors they found it "evident" he had septic shock and organ failure, describing him as "extremely ill".
Junior doctor Max Bacon, who had been qualified for just over a year, said he discharged Mr Mason after seeking guidance from a senior colleague and being "falsely reassured" by blood test results.
Dr Bacon, who said he had considered sepsis but a screening was not ordered, added: "I wish I had put him through the sepsis protocol.
"I see from hindsight he should have had it."
The coroner said he would be writing to the trust and NHS England about the problems highlighted during the inquest.
After the hearing, Mrs Mason said she hoped these issues would be "acted on with all seriousness" as she remembered her son as a popular man who was looking forward to his career and going travelling.
She said: "Our house used to be full of laughter and life. It is now quiet and we are all struggling.
"If changes are made that result in lives being saved, that will be of some small comfort.
"The conclusion was stated by the coroner that it was a treatment and diagnosis problem. He also found significant problems with the vaccination system."
Warning that "this is not just a local problem", she added: "Our fight is to ensure that every GP surgery across the country has the patient alert system switched on and offers the vaccine to all of their 18 to 25-year-old patients.
"We also hope that all hospitals update their sepsis protocols and make sure their staff are trained to follow them without exception."
In a statement, Paul Sankey, of the family's legal team, said: "For Tim's family nothing can make up for his loss, but the acknowledgement of responsibility will go a small way to helping them move on.
"We should now be able to resolve a legal claim on behalf of the family."
After the hearing Dr Peter Maskell, the trust's medical director, said: "We are truly sorry that we did not do everything that we could have clinically to help diagnose Timothy's sepsis sooner, and take steps to treat this diagnosis.
"I would like to personally apologise unreservedly to Timothy's family and friends for this tragedy.
"While no words can adequately address their loss, we will ensure that lessons are learnt by our doctors and nurses.
"We have carried out a full review of Timothy's care and have taken a series of actions to address areas of our practice that fell short of the high standards we want for all of our patients."
These include new protocols for the senior review of all patients due to be discharged from emergency units with abnormal observations.
The importance of following the trust's sepsis protocol, in light of Mr Mason's experiences, is also stressed to all medics during teaching sessions.