Councillors voted to reprieve the B-listed former gas holder on the Granton foreshore and criticised National Grid, which owns the structure, for allowing it to fall into disrepair.
It will now be urged to bring forward proposals to carry out millions of pounds worth of work to the gas holder, which was given protected status in 1998, and find an alternative use for it.
National Grid, which owns 110 acres of land in Granton, insisted the gas holder had "no possible alternative uses" and claimed the council's decision had rendered its plans for a new urban village in the area "undeliverable".
But councillors claimed the company had simply left the gas holder - which dates from 1898 and is the last remaining sign of Granton's once-booming gas industry - "to rot" over the past 12 years. They were also sceptical about its claims that the structure - last in use in 1987 - had become a health and safety risk and that keeping it would hamper future development of the Forthquarter area.
Heritage campaigners had pointed out that similar structures worldwide had been converted into conference centres, visitor attractions and apartment blocks. Historic Scotland also objected on the grounds that options for retention had not been fully explored and the developer did not have any plans for its replacement.
National Grid, which claims the repair bill will be at least 5.2 million, has never brought forward restoration plans and council officials said there was no evidence it ever carried out repairs on the listed structure.
Council officials admitted the firm had failed three out of four key tests to justify demolition, but still recommended approval of its application.
Principal planner Nancy Jamieson said: "It is an iconic building, it is very unusual in Edinburgh and it is of historical importance.
"The Edinburgh waterfront masterplan states it should be retained as an icon of the heritage of the area. We think it is capable of repair but the main issue is the cost that would involve. We are recommending approval with a heavy heart."
However, local Labour councillor Cammy Day, who addressed the planning committee, said: "This company has made millions of pounds from the number of flats that have been built on its land. The gas holder has been left to rot by them."
Liberal Democrat councillor Elaine Morris, one of those to vote against the demolition bid, said: "The gas holder provides a feeling of continuity with Granton's past. We mustn't under-estimate the historic connection.I don't see why they shouldn't get to grips with it."
Jim Moore, sales and lettings manager with National Grid, said: "The structure dominates and restricts opportunity to fulfil the development potential of the Forthquarter site.
"This enforced retention renders our vision to create an urban village undeliverable for the foreseeable future."