They were both seeded third, and both conceded only one set throughout the clay-court Grand Slam tournament at Roland Garros.
The 17-year-old Prizmic beat Juan Carlos Prado Angelo of Bolivia 6-1, 6-4 in the boys' final after the 15-year-old Korneeva earlier beat No. 6 Lucciana Perez Alarcon 7-6 (4), 6-3 to follow up her success at the Australian Open.
The 18-year-old Prado Angelo, seeded eighth, was bidding to become the first Bolivian player to win a junior singles title at a major. He failed to convert his two break points and dropped his serve three times.
Korneeva became the first girl to win two major titles in a season since 2013, when Ana Konjuh and Belinda Bencic both won two majors, and is the first girl to win the first two majors of the season since Magdalena Maleeva in 1990.
Korneeva had three aces and broke Perez Alarcon's serve six times. The 18-year-old Perez Alarcon double-faulted nine times and converted four of her nine break-point chances.
Perez Alarcon was the first girl from Peru to reach a junior final. Peru's Jaime Yzaga won the French Open boys' title in 1985, and Luis Horna lost the final at Roland Garros in 1997.
Both finals were held on Court Simonne-Mathieu.