In the match against Tsitsipas, Djokovic won the first two sets comprehensively, but the fifth-seed Tsitsipas staged a comeback and won the third and fourth set, sending the match into the fifth and final set.
For Nadal, it was a 99th win at Roland Garros since his 2005 debut and put him just one victory away from equalling Roger Federer's all-time record of 20 Grand Slam titles
Top seed and 2016 champion Djokovic won 6-4, 6-3, 6-3 against Russian 15th seed Khachanov to draw level with Rafael Nadal on a record 14 quarter-final appearances in Paris
On Sunday, 12-time champion Nadal produced another ruthless and dominant display as he dropped four games to complete a 6-1, 6-1, 6-2 win over American qualifier Sebastian Korda on Court Philippe-Chatrier.
He will be the centre of attraction whenever the French Open is being played. However, he is in the news for a different reason on Friday when he was playing his match.
Nadal, who is seeking a 20th Grand Slam title to equal Roger Federer's record, on Friday defeated Travaglia 6-1, 6-4, 6-0 in one hour and 35 minutes on a covered Court Philippe-Chatrier to register his 96th victory at Roland Garros.