Belhaven Pubs had wanted to open the Black Bull on Leith Street one hour later on both Friday and Saturday night.
The move did win some support on the city's licensing board but was eventually rejected on the casting vote of licensing leader Marjorie Thomas.
Police had called for the policy of only allowing pubs to open until 1am to remain.
But representatives for the bar argued that it is a "well established rock 'n' roll bar" with no previous problems.
Three out of the six councillors on the board had supported the application.
Labour councillor Eric Barry said: "If it was a hard rock 'n' roll cafe with fights every night we would say no. But it isn't."
Two other councillors voted with Councillor Thomas to reject the application, then she used her casting vote to reject.
She said: "If this was to be granted it would be granting a public house a license until 2am. It might send out a message that we do not want to send out."