Zakharov scored a total of 555.90 in the Aquatics Centre to get the better of China's Qin Kai and world champion He Chong.
Qin scored 541.75 to take silver ahead of compatriot and defending Olympic champion He, who grabbed bronze with a total of 524.15.
'I just can't believe it as of now. I have done it finally,' the Russian said.
Zakharov added: 'I came second in the semis in the morning but I promised myself that second place was simply not good enough.
'The last dive was my grand finale. I thank everyone here who has supported me in my ups and downs.'
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