Dr Isyaka Mamman, now thought to be 85, admitted gross negligence manslaughter over the death of Shahida Parveen, 48, at the Royal Oldham Hospital in 2018.
He used the wrong needle and inserted it in the wrong place, piercing the sac holding Mrs Parveen's heart.
Mrs Justice Yip at Manchester Crown Court said Mrs Parveen's death was his fault and sentenced him to three years.
She also criticised the NHS trust, pointing to the fact that Mamman had both lied about his age and had been involved in two critical incidents similar to that which led to Mrs Parveen's death.
The court heard Mrs Parveen attended Royal Oldham Hospital on 3 September, 2018, to give a bone marrow sample.
This is usually taken from the hip bone but, after failing in his first attempt, Mamman tried to instead take it from her sternum.
This was a "highly dangerous" procedure, the court was told, and one which had led to another of Mamman's patients being permanently disabled three years earlier.
A formal complaint was made to the hospital in 2015 after a patient complained Mamman had used "excessive force" during a bone marrow biopsy.
The unnamed patient was told that Mamman was "in his 70s" and his colleagues thought he should retire but they could not dismiss him purely because of his age.
She was assured he would be put on light duties in the future.
The court went on to hear that Mrs Parveen lost consciousness as soon as the needle was inserted and pierced her pericardium, also known as the heart sac, causing massive internal bleeding.
Her husband ran from the room shouting: "He killed her. I told him to stop three times and he did not listen. He killed her."
Haemotologist Mamman qualified as a doctor in Nigeria and had worked in the UK since 1991.
He was employed by Pennine Acute Hospitals NHS Trust from 2004 until Mrs Parveen's death.
Mamman's "true age" is a matter of "controversy", the court heard, since his birthplace in rural Nigeria had no system of birth registration.
During his medical training, he said he was born on 16 September, 1936, meaning he was 21 when he began his training as a doctor, qualified in 1965, and was 81 at the time of the fatal incident.
But he also told NHS bosses that he had been born in 1941 - suggesting he commenced his medical degree aged 16.
And in 2001, when approaching the then compulsory retirement age of 65, he adopted an even later birth date of October 1947 when applying for naturalisation as a British citizen.
This would have meant he had been only 10 when he started his medicine degree.
In 2004 Mamman was found guilty of serious professional misconduct by the General Medical Council (GMC) and suspended for 12 months for lying about his age.
The Pennine Trust sacked him but then rehired him in 2006 after he had been restored to the register by the GMC, who accepted his date of birth to be 1943.
This would suggest he would have been only 14 or 15 when he began his training.
Mamman gave no reaction as he was sentenced, but members of his family wept in the public gallery.
Mrs Justice Yip said it was "hard to understand" why the previous serious incidents had not led to Mamman's retirement from medicine, and said there had been "failings in the system".
Dr Chris Brookes, deputy chief executive for the Northern Care Alliance NHS Foundation Trust, which now runs the Oldham Royal Hospital, said: "We wish again to offer our sincerest condolences to Mrs Parveen's family and friends and we are deeply sorry for their loss."
He said the trust had admitted liability in relation to a civil claim brought by the family.