Djokovic reached his 225th tour-level quarter-final by claiming his first victory over Alejandro Tabilo in Athens.
Following his win, tournament organisers played a tribute video to his former coach Nikola Pilic, who died in September aged 86.
An emotional Djokovic said: “Considering what he meant to me and my family – privately, also professionally – he was my tennis father, someone who has played a fundamental, integral role in my development as a tennis player and as a human being.
“It was really sad news when I heard that he passed away.
“As long as I play tennis and as long as I live, I’ll celebrate his name.”
Chile’s Tabilo had won both previous meetings with Djokovic, but Roger Federer remains the only player to record a 3-0 head-to-head start against the record 24-time men’s Grand Slam champion.
But after prevailing in a first-set tie-break, the 38-year-old Serb extended his record of winning every match in which he has won the first set this season to 28 as he cruised to a 7-6 (7-3) 6-1 win.
Djokovic won 20 of the final 23 points in a dominant finish to the match.
Chasing the 101st singles title of his career in the Greek capital, Djokovic will next play Nuno Borges on Thursday after the Portuguese sixth seed pulled off a comeback 5-7 6-3 6-4 win over American Eliot Spizzirri.