Billy White, a Christian, and Muslim Gary Lindley prayed after the pre-planned killing of Brett Rogers, which they believed would "exorcise a demon" from him and "cleanse" him of his crimes.
Worcester Crown Court was told staff at HMP Long Lartin were then handed a note saying the killers had decided to "free" their victim from "darkness".
White, aged 24, was given a whole life term for the killing - carried out while he was already serving a life sentence for the 2015 murder of his partner.
Judge Robert Juckes QC heard that White was jailed for at least 15 years at the Old Bailey in May 2016 after murdering his partner by stabbing her through the neck as she slept at their home in Hayes, west London.
Lindley, aged 42, was serving an indeterminate sentence after being jailed at Nottingham Crown Court in 2007 for his part in a violent distraction burglary.
Ordering Lindley to serve a minimum term of 17-and-a-half years for killing Rogers, Judge Juckes ruled that the prisoner's murder had not been committed in the "furtherance of a religious cause".
The judge said White and Lindley - who pleaded guilty to murder at an earlier hearing - had admitted during police interviews that they had decided to kill Mr Rogers around a week before his death.
Addressing his reasons for handing White a whole life term, the judge said: "This is his second offence of murder.
"This was a determined and premeditated killing of a particularly cruel kind of a man in his own cell by two men who overpowered him.
"They picked on him because of what they had come to believe about him."
Rogers, from Stansted Mountfitchet in Essex, was jailed for life last year with a minimum term of 32 years for the murder of his mother and her friend.
Opening the facts of Rogers' murder, prosecutor Benjamin Aina QC said prison officers found the 25-year-old's body on June 7 after he failed to collect medicine.
The killing - the fourth homicide at Long Lartin in the past five years - took place between 3.21pm and 3.54pm when CCTV captured White and Lindley entering and leaving his cell.
Paramedics pronounced Rogers dead at 6.24pm and while the wing was in lockdown, Lindley passed a note to a prison officer reading: "I was ordered by the Lord My God to free Brett Rogers. I know you will not see it this way but that is between you and God. I am of sound mind. Please can I speak to the Governor."
During their police interviews, Lindley and White, who worked as support cleaners at the maximum security jail, said they had tried to "snap" Rogers' neck and then suffocated him with a pillow because he did not appear to be dead.
According to his account to police, White then used a blue marker pen to draw yin and yang signs on the dead man's cheek.
Before the sentencing, Lindley tried unsuccessfully to withdraw his guilty plea via a prison video link, citing mental health issues.
The court heard Lindley was first jailed at Nottingham Crown Court in 2000, receiving a 15-month sentence for a violent offence.
He was then given a further term of custody at the same court in 2002 for an attempted robbery and possession of an offensive weapon in a public place.
