The 17-year-old from Kyoto is in third place in the prestigious six-man competition.
Lucas Broussard of the United States is the leader with 81.11 points, while Italy's Nikolaj Memola is in second with 79.84. Nakamura's score in third is 74.81.
Nakamura skated to "El Conquistador" as the junior men kicked off the competition at Palavela Arena and exuded confidence throughout his program. He opened with a nice triple axel, followed by a solid triple loop, and added a triple lutz/triple toe loop combination. Nakamura received level fours on two of his spins and a level three on his step sequence.
"I am very happy that I was able to perform without mistakes on this stage," Nakamura was quoted as saying.
His showing was certainly a relief for him after finishing fourth at the Japan Junior Championships in Hitachinaka, Ibaraki Prefecture, in November.
Yoshioka, Japan's junior champion, skated to "Malaguena" and began with a clean triple axel.
He struggled from there, however, doing a three-turn out of the landing on the front end of his triple lutz/triple toe loop combo. Yoshioka's triple loop was also shaky, and he could only notch just one level four on his spins.
"I was able to land the triple axel, but it wasn't the same jump as usual, and I failed the lutz/toe and the loop," Yoshikoka commented.
He added, "I'm really disappointed."
Takeru Kataise competes in the men's short program portion of the Junior Grand Prix Final. (KYODO)
Kataise had a calamitous skate from the outset, going down hard on his opening triple axel, then falling again on his planned triple lutz/triple toe loop combo. The 18-year-old posted level fours on two of his spins, but the damage was done.
"Right now, I still feel like I can't accept the reality," Kataise remarked. "To be honest, I'm filled with a lot of sadness."
The author is a veteran sports journalist and one of the world's foremost figure skating experts. Find articles and podcasts by Jack on his author page, here, and find him on Twitter @sportsjapan.