Rangers in the first derby of the season, with Filip Helander's goal condemning them to a second defeat in four league games.
It was a first taste of the fixture for new manager Ange Postecoglou, with opposite number Steven Gerrard at home isolating with Covid.
A positive first half should have seen the visitors go ahead, but Odsonne Edouard fluffed his lines when teed up by Kyogo Furuhashi.
And a set piece mix-up in the second half gave Helander the chance to score the only goal of the game and send the Ibrox crowd wild.
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