Dr John Sentamu told peers: "I am one of those who believe that human beings are psychosomatic spiritual entities."
The archbishop then told how he freed the spirit of a young girl, left petrified by seeing a goat sacrificed.
During a debate on an amendment he said: "Illness can be physical or mental but it can also be spiritual."
The amendment, tabled by psychiatrist and crossbench peer Baroness Hollins, called for the words to be inserted into a clause about the duty of the secretary of state, the NHS Commissioning Board and clinical commissioning groups to improve the quality of services.
Making his case, the Anglican archbishop argued that schools now emphasised students' spiritual dimensions, and said hospital chaplains' work addressed spiritual issues, as well as the physical and mental.Witches' coven
He also told how when he first became a vicar in south London, he was invited to a home where there was "a presence", a phrase he said he did not understand at the time.
At the home, he said, he found a young girl who had been unable to move for nearly three weeks and would shout out in the middle of the night.
He was told the family had been to a witches' coven where a goat had been sacrificed. The young girl was petrified she would be next.
Visits from a GP, psychiatrist and psychologist did little to help, he said, but then he said a prayer, anointed the girl and lit a candle on his visit.You can see the Archbishop's contribution 3hrs 23mins into this video
Shortly after, he received a phone call saying the girl was no longer terrified and was talking again.
"That was not mental or physical illness; there was something in her spirit that needed to be set free," he told his peers.
Dr Sentamu, 62, acknowledged the importance of highlighting mental and physical illnesses, but asked whether they needed to be spoken of "in almost separate categories" in the bill.
"I do not want to divide up a human person. Therefore, I believe that the bill covers people's needs without inserting the words 'physical and mental'.
He said he was "content" that the bill, as it stood, covered all aspects of the human person simply by using the word "illness" .
"The element of the spiritual well-being of people is not on the face of the bill but I am absolutely convinced that, as it stands, my needs would be taken care of because it talks about 'the prevention, diagnosis or treatment of illness'."
The Health and Social Care Bill, if passed, would see GPs and other clinicians given much more responsibility for spending the budget in England, while greater competition with the private sector would be encouraged.