Patients in England and Wales will be offered extra checks using a mobile device that records blood pressure over 24 hours, says the watchdog NICE.
A quarter of patients may find visiting a GP stressful, leading to misdiagnosis and being given drugs they do not need.
The move could save the NHS £10.5m a year, predictions suggest.
High blood pressure (blood pressure of 140/90mmHg or more) affects about a quarter of all adults in the UK. It is a leading risk factor for heart disease or stroke and costs the NHS about £1bn a year in drugs alone.
Currently, most patients found to have high blood pressure for the first time are given a formal diagnosis if their blood pressure is raised at two subsequent visits to the doctor.
They may then be prescribed medication to lower their blood pressure.
Research suggests, however, that about a quarter of patients actually have "white coat" hypertension - where blood pressure is raised temporarily due to stress.
Now, the National Institute for Health and Clinical Excellence (NICE) has advised doctors in England and Wales to move towards "ambulatory" monitoring of patients at home, using a device that automatically takes blood pressure readings every 30 minutes day and night.
Around one in 10 GPs are already offering ambulatory monitoring, either directly or by referring patients to a hospital specialist.
The new guidelines were issued at the same time as the publication of a research study in The Lancet.
One of the authors of the paper, Professor Richard McManus of the University of Birmingham, said: "This research shows that ambulatory blood pressure monitoring at the time of diagnosis of high blood pressure would allow better targeting of treatment and is cost-saving.
"Ambulatory monitoring is already available in some general practices and we have shown that its widespread use would be better for both patients and the clinicians looking after them.
"Treatment with blood pressure lowering medication is usually lifelong and so it is worth getting the decision to start right in the first place."
It is expected to take about a year to implement the advice at a net cost of about £2.5m. However, in the long-term the costs will be recouped, say experts, eventually saving about £10.5m a year.
Cathy Ross, senior cardiac nurse at the British Heart Foundation, said the number of people with high blood pressure in the UK was "staggering".
"Some 12 million people are diagnosed with the condition and it is estimated another 5.7 million people have it but are unaware. It's a major risk factor for heart disease and strokes so it's crucial we do all we can to get people diagnosed and properly treated as soon as possible.
"This new guidance will refine the way we test and treat people for hypertension, particularly by helping to identify people suffering from 'white coat hypertension'.
"It doesn't mean that current methods aren't working, only that they can be improved further. Anyone currently concerned about their blood pressure or treatment should speak to their GP or practice nurse."
Professor Bryan Williams from the University of Leicester, chairman of NICE's Guideline Development Group, told the BBC there would be an "upfront cost" of introducing the ambulatory equipment.
But he added: "When you offset that against the reduced treatment costs of people who don't require treatment, and the reduced number of visits to doctors, we estimate that the NHS within about four or five years will save £10m.
"So it's a win-win situation for patients because it's a better way of making a diagnosis and the NHS actually saves money."
British Hypertension Society president Professor Mark Caulfield said the move was supported by research.
He said: "We've recommended that if high readings are found in the practice, that a 24-hour blood pressure monitor is worn because we found that the evidence now makes it very clear to us that this is a much more precise way of diagnosing high blood pressure."
In response to the new guidelines, Health Minister Anne Milton said: "These guidelines show that the use of innovations such as ambulatory monitors can provide more accurate blood pressure readings for patients as they go about their daily lives.
"This is not only better for patients, but also a better use of NHS resources."
Patients thought to have high blood pressure should have the diagnosis confirmed at home, according to new guidelines.