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."

Researchers from Trend Micro found blogs on the website had been modified to install malware known as Cryptesla on readers' devices.
The malware holds files on the host machine to ransom and demands a payment to restore them.
The Independent said it had removed all ads on the site while it investigated.
"It appears that an advert appearing on that blogsite may have included malware," said a spokesman for the newspaper.
"There is no suggestion or evidence that any of our users have been affected by this."
The spokesman said the site affected was an old or "legacy" system that was now rarely visited.
According to Trend Micro, the ransomware has been present on the Independent blogs website since at least 21 November.
"We reported it to them on Tuesday - but, as of today, it is still happening," said Raimund Genes, chief technical officer at Trend Micro.
"Now we need to go public to warn people who are not using security software like ours."
The malware exploits a security hole in Adobe Flash Player to install itself on a victim's computer.
Once downloaded, it sets about encrypting documents, rendering them useless without the key to decrypt them, for which it demands a ransom.
The vulnerability in Flash has since been patched, but anybody using an old version of the web browser plug-in could still be at risk.
"For a while on Tuesday, the malware didn't trigger. But that was not the Independent solving it, it was the attackers updating the malware with a new version," said Mr Genes.
"My advice is to update your Flash Player. Always do it immediately when it says an update is available, because Flash remains one of the main ways attackers can compromise a system."
The spokesperson added that the media group was now looking into the incident.
"We are currently investigating third-party advertising suppliers that are used by our externally hosted blog platform Independent blogs, which is a separate entity to independent.co.uk," they said.
"Less than 0.2% of the Independent digital audience visited this separate, legacy blogsite in the entire month of November," the spokesman added.
More and more cyber criminals are seeking to subvert adverts in a bid to catch out visitors to popular sites.
This so-called malvertising has been found on many other places. Other newspapers as well as streaming sites and porn hosts have all briefly hosted booby-trapped ads.
A Derby swimming pool threatened with closure is to remain open for another year, council bosses have confirmed.
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The Independent newspaper's blogging platform has been briefly compromised with malware that infects readers' computers, security experts have said.