Sakamoto meanwhile has to settle for silver as her stellar career ends without an Olympic crown.
She is retiring aged 25 having won three world titles and bronze at Beijing 2022.
Her final performance here was to Non, je ne regrette rien by Edith Piaf, and Sakamoto must have no regrets about a performance in which all 12 elements were given positive grades of execution.
But it scored five points lower than Liu in the technical elements, with the American’s routine judged to have been more challenging.
Sakamoto wept as she left the ice, but by the medal ceremony rightly looked delighted with another major honour.
“I wasn’t able to give absolutely everything,” she said after the event. “I was aiming for the gold medal. The frustration of not being able to win it is really hitting me right now.
“I thought I might be able to finish with a smile, but instead I’m ending it with this sense of frustration. Still, I think feeling this way will be important for the rest of my life.”
That initial disappointment was in stark contrast to the joy of compatriot Nakai, who ends a phenomenal debut campaign with an Olympic medal.
The youngest skater in the competition, Nakai stormed to the top of the leaderboard following the short program and opened her free skate with a triple axel – a brutally tough element she is now making her trademark.
But Nakai stumbled on her triple lutz, which played a major role in knocking her down below Liu and Sakamoto.
