"I'm very proud, but it means I'm not young!" said the 36-year-old Serb of the record, achieved by playing his "best tennis since the beginning of the tournament".
"I'm putting in a lot of effort and I'm very motivated to keep going," he said.
Rafael Nadal has played 16 quarters in the Paris Major he has won 14 times, as Djokovic aims for a third title to bring the record for Grand Slam titles to 23.
The Serb, ranked 3rd in the world, is about to play his 55th quarter-final in a Grand Slam tournament (the record of 58 is held by Roger Federer and Nadal has 47). He has always reached the quarters in Paris since 2010.
To reach the last square, where the long-awaited duel against the world No. 1 and another big favorite of the tournament Carlos Alcaraz could occur, he will first have to dismiss Tuesday the Russian Karen Khachanov (11th), who eliminated the Italian Lorenzo Sonego (48th) 1-6, 6-4, 7-6 (9/7), 6-1.
Varillas was playing for the third time in the main draw of a Grand Slam tournament and had never won a match in such a tournament.
He was the first Peruvian to reach the 8th finals at Roland-Garros since Jaime Yzaga in 1994.
"I knew he was a clay court specialist and you have to earn every point," Djokovic said of Varillas, whom he clearly dominated in less than two hours.
© 2023 AFP