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Crews were called about 6pm to the unit in a Stafford St complex.
Neighbour Quillan Gutberlet said he heard the smoke alarm sounding for some time, went to investigate, saw flames beginning to lap at the walls of the unit's kitchen and called 111.
The fire appeared to have been started by a pressure cooker. The couple who lived in the flat were not home at the time, he said.
Firefighters were seen running to the building and donning breathing apparatus before entering.
Fire and Emergency New Zealand shift supervisor Mau Barbara said the blaze was contained without issue.
However, it had caused significant damage and the residents would have been unable to return last night, he said.
Appliances from St Kilda and Roslyn stations and a turntable ladder truck from Dunedin City attended.