National Institute of Health and Care Excellence guidance urges medics to consider sepsis early on when treating any patients unwell with infections.
The problem, caused when the body's immune system overreacts to infection, leads to 44,000 UK deaths a year.
But experts estimate between 5,000 and 13,000 could be avoided.
Sepsis can lead to severe organ failure, shock and death if not treated early enough.
But initial symptoms - such as a rapid breathing or feeling generally unwell - can be vague, making it difficult to set apart from other conditions.
In its first guidance on the issue, NICE acknowledges it is a complex medical problem.
But the health watchdog says GPs, paramedics and hospital staff must make "Could this be sepsis?" the first consideration for anyone unwell with an infection - in much the same way that medics consider the possibility of a heart attack for patients with chest pain.
Prof Mark Baker, from NICE, told the BBC: "The problem with those patients who died unnecessarily of sepsis is that staff did not think about it soon enough."
He added: "This is complicated medicine.
"It requires a depth of thought and experience and a way of examining patients which isn't always there - particularly because of time pressures and partly because we have got used to implementing guidelines without thinking."
Cornwall mother Melissa Mead, whose one-year-old son William died from sepsis in 2014 after potential signs of the condition were missed by NHS 111 staff and GPs, welcomed the move.
She added: "This could not come any sooner. Sadly we have been touched in very real terms by sepsis and could not agree more that clinicians need to start asking: 'Could this be sepsis?'"
Sepsis happens when the body's immune system - the way the body responds to bugs and germs - goes into overdrive.
The initial problem can be quite mild and start anywhere - from a cut on the finger to a chest or urine infection, for example.
But when the immune system overreacts, this can lead to an unintended but catastrophic attack on the body.
If left untreated, this sets off a cascade of reactions - from shock to organ failure and even death.
There is a lot of research going on to attempt to find out what exactly triggers this sometimes fatal reaction.
Read more: Why can sepsis be so hard to spot?
Meanwhile, Dr Maureen Baker, of the Royal College of General Practitioners, said: "The diagnosis of sepsis is a huge worry for GPs, as initial symptoms can be similar to common viral illnesses, so we welcome any guidance or support to help us identify it as early as possible."
The guidelines say patients with possible sepsis should be sent to hospital in an ambulance and treated urgently by senior staff.
Separately, NHS Improvement has launched an initiative to tackle children's health.
It encourages parents to speak up if their child's health is deteriorating and urges staff to work more closely with parents.
Dr Mike Durkin, NHS national director of patient safety, said: "Time and time again, and is some cases tragically too late, we see that some children could have received better care if healthcare providers worked with parents to understand and treat deterioration in health.
"There have been far too many cases covered in the media on the failure to treat sepsis that have highlighted the sad and frustrating instances of parents repeatedly flagging concerns about their children."
Suspected sepsis in patients must be treated as an emergency in the same way as heart attacks are, England's health watchdog says.