Zevallos came from the youth ranks of Universitario de Deportes, arriving from his natal Ica to Lima at 14 years of age to live at Estadio Lolo Fernández.
[1] In 2017, he was observed by manager Pedro Troglio while playing in the Torneo de Promoción y Reserva and was invited to train with the first team.
In 2018, manager Nicolás Córdova promoted Zevallos to the first team, after which he made his professional debut in an away match against Sport Huancayo and played a total of six games in the season.
He played more regularly in 2021, in a total of 13 matches between the league and the Copa Libertadores, but without standing out.
[2] Zevallos has played for Peru at the U20 level, being called for the 2019 South American U-20 Championship.