The play, called Restored, was put on by inmates at the Marshgate jail for an audience of criminal justice professionals, inmates, and students from the Central School of Speech and Drama, who had given them some acting tips.
They spent four weeks polishing their performance - rehearsing for up to seven hours a day.
The aim of restorative justice is to give offenders the chance to meet or communicate with the victims of their crimes in a bid to aid their rehabilitation.
Cat Jones, senior manager arts and media at the prison, said:
"This is a powerful tool in reducing re-offending because it encourages offenders to think about the negative impact they have had upon other people's lives. It also gives the victim the opportunity to take back control of the situation by giving them a voice."
The play, acted out by 11 inmates, told the story of two prisoners who had committed a knife attack and a burglary and later met their victims at mediation sessions.
At the end of the performance prisoner 'J' spoke to the audience about his experience of restorative justice.
The play was acted out on one of the prison wings.
It is the third performance of its kind at Marshgate, which is the only jail in the country to employ a senior manager to develop the arts.
Prison director John Biggin said: "The piece is perhaps the most challenging and thought-provoking we have undertaken to date and the production team has put together a piece which is both groundbreaking as well as being without precedent in terms of what can be achieved in prison, by prisoners. This is truly an example of delivering a Reducing Re-offending Revolution and is prison reform in action."