Hospitals in England will be offered funding from April to introduce "Martha's rule", the NHS has announced.
The government has backed plans to roll out a system giving seriously ill patients easy access to a second opinion if their condition worsens.
About two-thirds of hospitals - at least 100 - will initially be able to apply to participate in the scheme.
It follows a campaign by the parents of Martha Mills, 13, who died of sepsis because her symptoms were missed.
Martha's mother, Merope, told BBC News the new system would save lives and mean her daughter had not died "in vain".
Ms Mills previously said she and her husband, Paul Laity, had been ignored when they had raised concern about Martha's care and asked for her to be transferred to intensive care.
Under the new scheme, acute hospital will receive government funding for posters and leaflets informing patients and their families they could directly ask a team of critical-care medics for a "rapid review" of treatment, NHS England said.
Medics will also formally record families' observations of a patient's condition or behaviour.
Ms Mills said she was "pleased", because patients and families had a "role to play".
"Sometimes, doctors are incredibly overstretched," she told BBC R4's Today programme.
"And they cannot always spot the same changes in a patient that family and patients themselves can."
The new system would have saved Martha's life, Ms Mills said.
Martha was admitted to King's College Hospital, south London, in 2021, after injuring her pancreas slipping on to the handlebars of her bike while cycling.
She later developed sepsis - but with better care, could have survived, an inquest found.
The hospital apologised for its mistakes.
Ms Mills said: "We told three different consultants that we were worried about her and we were just told she would be fine and this was a normal infection she had.
"And when I had my doubts, still, I had nowhere to go. There was no ripcord to pull. I just had to trust the doctors."
Patients already have the right to a second opinion if their condition deteriorates - but trusts currently operate different systems.
Challenging doctors could be "difficult", Ms Mills said. And without the new scheme, many patients and their families would not know how.
NHS England chief executive Amanda Pritchard said: "NHS teams have been piloting ways to better identify and respond in these cases, over the last year, and the rollout of a national programme to give patients and families 24-7 access to a rapid clinical review will now help ensure that those experiencing acute deterioration can be identified and treated much more quickly.
"While the need for escalation will hopefully only be needed in a small number of cases, I have no doubt that the introduction of Martha's rule has the potential to save many lives in the future."
The scheme rollout would be evaluated over the next year and may be followed by further funding to include all acute hospitals, NHS England said.
Proposals to adapt it for community hospitals and mental-health trusts are also being considered.