Ki, the top seed and world number two, was pushed all the way by Roman and after drawing 5-5 across five sets, the Olympic title was decided one shot apiece.
Ki drew first and hit a disappointing eight that crept high, but with nine needed to complete a huge upset Roman's arrow veered left and ended further out in the eight ring.
Roman goes home with the silver medal and fellow Mexican Mariana Avitia won bronze after beating Khatuna Lorig of the USA in their match.
Republic of Korea's women won every individual gold between the Los Angeles 1984 Games and Athens 2004 but had to settle for silver and bronze at Beijing 2008.
I have never felt that lucky but the gold was meant for me
Ki Bo Bae
Ki, who now has two golds having been part of a triumphant three-string team on Sunday, was not at her imperious best on a day when inconsistent winds made it hard for the competitors to produce solid groups, but she did enough to take a 6-5 victory in the most tense of finales.
Speaking tearfully after the Victory Ceremony, Ki said: 'I have been training so hard so I did not feel too much pressure. But there was a big wind when I came to shoot and I was embarrassed, very embarrassed.
'It (an eight) would have been a big surprise to the spectators here and to everyone watching in Korea.
'I wasn't even watching when Aida took her last shot, I was just praying hard. I have never felt that lucky but the gold was meant for me.'
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