Oates defeated Israel's Bar Raufman before losing to Mongolia's Altansukh Dovdon to enter the repechage.
He returned to winning ways however and beat Tornike Tatarashvili of Georgia by ippon to reach the bronze-medal match.
And Oates upset the home crowd against Turkey's Sinan Sandal as he won by waza-ari followed by a hold down for ippon.
Ashley McKenzie, who liked Oates competed at the London 2012 Olympics, won his first fight in the -60kg but lost his second.
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