The 17-year-old landed a triple Axel in a spirited skate and posted a season-best 78.71 in her Olympic debut.
Three-time world champion Kaori Sakamoto was second with 77.23, while American Alysa Liu earned 76.59 to sit third heading into Thursday's free skate, which will decide the medals.
"I wasn't nervous at all, so I was able to perform as my usual self and excel," Nakai told reporters.
"Since this is my first Olympics, I had nothing to lose, and that mindset definitely translated into my results."
Nakai said she drew inspiration from Japan's pairs champions Riku Miura and Ryuichi Kihara, who staged a comeback from fifth place in the short programme to win gold on Monday.
"I was deeply moved by the pairs performance yesterday, and it really brought home to me how important it is to never give up until the very end," she said.
Sakamoto, chasing a gold-medal finish to what she has said will be her final Olympic campaign, leaned on her experience in front of a sold-out crowd at the Milano Ice Skating Arena, delivering a composed, polished routine to "Time To Say Goodbye."
"I wanted to be myself as usual, and there was a little bit of nerve, but I was able to sustain the nerve," said Sakamoto, the bronze medallist from Beijing 2022.
"In the first half, I was a little bit anxious. But as the music goes on, I got very comfortable, and I was able to really enjoy my performance today."
Liu, the reigning world champion competing at her second Olympics, left the ice smiling after a confident skate marked by clean execution.
The American, who retired in 2022 at age 16 before returning to competition with a new perspective, was unburdened by the weight of expectations on Tuesday.
"A medal? I don't need a medal," she told reporters.
"I just need to be here, and I just need to be present, and I need people to see what I do next."