The Lausanne 2020 Youth Olympic champion leads from perennial rival Andrei Mozalev with Andrew Torgashev rounding out the top three in Tallinn.
With quads not permitted in the short program, Kagiyama scored 85.82 - 13 points higher than in Lausanne - to hold a narrow advantage over Russia's Andrei Mozalev going into Friday's free skate.
Andrew Torgashev of the United States was third on the day, ahead of Estonia's Aleksander Selevko who delighted the home fans with a career-best skate.
Junior Grand Prix Final winner Sato Shun lies fifth just ahead of Italy's Daniel Grassl.
Sato was the first of the big names to go, skating in the fourth group out of six.
Sato showed he is no back number with a fine short program, starting with a triple Axel followed by a slightly sketchy triple Lutz-triple toe loop combination and then a better triple loop.
He was rewarded with a new personal best score of 79.30.
Mozalev skated third in the penultimate group and produced another solid, clean routine.
The Russian - who led after the short program in Lausanne before having to settle for silver - landed a triple loop and a triple Axel followed by a triple Lutz-triple toe loop combo.
He also posted a new personal best, scoring 84.31 to take the lead.
Mozalev led until the final group with 17-year-old Grassl, who finished fourth at January's European Championships after a superb free skate, moving into third place with 78.91.
Then came Kagiyama whose third place at December's Japanese senior nationals has been the springboard to a spectacular 2020, culminating in another podium finish at the Four Continents.
The 16-year-old's jumping was immaculate as, like Mozalev, he landed a triple loop followed by a triple Axel and then a triple Lutz-triple toe loop combination.
It was another superb skate from the youngster and he earned his best short program score in junior competition to take the lead by just over one and a half points.
Selevko gave the home crowd plenty of reason to cheer as he scored a personal best of 80.87 to go into third place.
He was displaced by Torgashev who was the last to go.
The 18-year-old American performed superbly with his slightly lower technical elements score - a triple flip-triple toe loop combo performed mid-routine rather than Kagiyama's triple Lutz-triple toe loop as the last jumping element - stopping him challenging the big two.
But he will be delighted at a clean skate with a career-best of 81.50 leaving him in third ahead of Friday's free skate.