Djokovic has made headlines for his comments about Kosovo this week but his on-court progress has been relatively serene, reaching the second week without dropping a set.
The Serb star was made to work hard by Spanish 29th seed Alejandro Davidovich Fokina, who served for the first set and missed a set point in the second, but won 7-6 (7/4), 7-6 (7/5), 6-2 on Court Philippe Chatrier.
"A win is a win, maybe a bit too much -- the first two sets," said Djokovic. "I thought if I lost the second set we would play five hours today, but I'm proud of the performance."
Two-time champion Djokovic, who has also made the French Open quarter-finals in each of the past 13 years, will take on either Polish 13th seed Hubert Hurkacz or Peru's Juan Pablo Varillas in the last 16.
The 36-year-old is hoping to break out of his tie with injured rival Rafael Nadal at the top of the men's all-time list of major winners at Roland Garros.
He is just one title behind Serena Williams' mark of 23 Slams and two adrift of Margaret Court's overall record.
Djokovic has now won three of his four matches with Davidovich Fokina.
The first two sets lasted two hours and 47 minutes, as Davidovich Fokina provided a stern test of Djokovic's form.
But the world number three broke when he trailed 6-5 in the opening set before overturning a 3-1 deficit to win a tie-break.
Davidovich Fokina missed one set point to level the match before Djokovic won another breaker.
Djokovic then made short work of the third set.
World number one Carlos Alcaraz, considered the favourite and slated to meet Djokovic in the semi-finals, features in the night-session match against talented Canadian Denis Shapovalov.
The 20-year-old Spaniard has defeated players ranked outside the top 100 in his
first two matches.
Shapovalov is of a far higher calibre, though, despite struggling for form in recent months.
The Canadian was ranked in the top 10 less than two years ago and was a Wimbledon semi-finalist in 2021.
- Sonego stunner -
Italian Lorenzo Sonego battled back from two sets down to knock out Rublev and reach the last 16 for the second time.