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2020–2021: ATP & Olympics debut

Varillas made his ATP debut at the 2020 Chile Open as a lucky loser where he reached the second round by defeating Filip Horansky before losing to Albert Ramos Viñolas. The following year at the same tournament he reached the quarterfinals as a qualifier where he lost to top seed and eventual winner Cristian Garín. Varillas qualified to represent Peru at the Summer Olympics.

2022: Grand Slam & top 100 debut

At the 2022 French Open he qualified to make his Grand Slam main draw debut but lost to ninth seed Félix Auger-Aliassime.

He reached the quarterfinals at the 2022 Swiss Open Gstaad as a qualifier defeating top-20 player and third seed Roberto Bautista Agut before losing to Dominic Thiem. He also reached the round of 16 at the 2022 Generali Open Kitzbühel where he lost to fifth seed Albert Ramos Viñolas. As a result, he made his debut in the top 100, as one of the five Peruvian men to achieve the feat, at a new career-high of world No. 97 on 1 August 2022.

2023: Australian Open debut, first Major wins & fourth round, top 60

At the Australian Open he entered for the first time into the main draw at this Major as a lucky loser but lost in the first round to former top-2 player and twelfth seed Alexander Zverev. At the 2023 Argentina Open he reached the round of 16 as a qualifier defeating João Sousa. Next he defeated former top-3 player wildcard Dominic Thiem to move into the quarterfinals. He reached his first ATP semifinal with his second win over a top-20 player and third seed Lorenzo Musetti. As a result, he moved 20 positions up and reached a new career high ranking in the top 80 on 27 February 2023.

At the French Open, Varillas came from two sets to love down to defeat Shang Juncheng and win his first Grand slam match. He then defeated 19th seed Roberto Bautista Agut in five sets also from two sets to love down. He recorded the biggest victory of his career by ranking defeating 13th seed Hubert Hurkacz also in five sets to reach the fourth round for the first time at a Major. He became the first Peruvian to reach the fourth round of Roland Garros in 29 years since Jaime Yzaga in 1994. He reached a new career-high ranking in the top 60 on 26 June 2023.