Kagiyama, Yoshida put Japan on top at Finland Grand Prix
Kagiyama, the 2022 Olympic silver medallist and winner of the recent NHK Trophy in Tokyo, scored 103.97 points to edge ahead of compatriot Kazuki Tomono (90.78 points).
"Today I was little worried about my tiredness, as it was a very short time between the competitions," said Kagiyama after skating to "Sound of Silence".
"However, I gave a performance today and I will try to do the same tomorrow. There are so many talented skaters here and they motivated to me to do well."
He added: "I made a mistake at the NHK Trophy on the quad flip, so tomorrow I'll try to do better."
France's Kevin Aymoz, second at Skate America last month, was third with 85.13 points.
In the women's event, Yoshida, who finished third at Skate Canada in October, led the way with 67.87 points.
Italy's Lara Naki Gutmann (67.06) and Sarah Everhardt of the United States (66.28) filled out the top three.