Derby City Council wanted to shut Moorways Pool from April in a bid to save about Â£350,000 a year.
The Labour-led authority, which needs to save Â£79m over the next three years, said it had found the savings by making cuts in other areas.
Campaigners who gathered more than 4,000 signatures on a petition said they were delighted at the news.
Ranjit Banwait, leader of the authority, said the council had committed to keep it open for a year.
He said the council had identified savings "in back-office areas" and a restructuring of management jobs, which had been "untouched" since 2010.
However, he stressed if the authority failed to get a "fair deal" from central government in the future, the pool would still have to close.
Campaigners had accepted the pool, which is 33m in length, was in need of repair.
There are plans for a new 50m pool to be built by 2018 to replace it.
However, closing it would have left only one other public pool in the city - the Queen's Leisure Centre, they said.
Doug Whitlam, of the Derbyshire Amateur Swimming Association, said: "One of the main things for me would have been the loss of teaching.
"Twelve hundred young people use this facility every week and that would be lost forever."
A Derby swimming pool threatened with closure is to remain open for another year, council bosses have confirmed.