The Atkinson Secure Unit in the city was set to close following the Youth Justice Board's decision in March not to renew its contract.
But Devon County Council has now agreed to maintain the unit until March next year as a slimmed-down operation. Its future will be reviewed again next year.
The move still means job losses for the unit but the council has pledged to save 40 of its 85 jobs.
Until March, the unit will operate eight of its 11 beds for a mixture of court and welfare cases from within the county and other councils.
John Smith, Devon County Council's executive councillor for children's services, said the centre was being maintained as it had built up a reputation around the country for good quality care.
"It is not beyond our grasp to extend this reputation by establishing an innovative working arrangement that could be a centre of excellence for meeting the needs of troubled young people," he said.
