Serving down 15-40, Djokovic then netted an inside out crosscourt forehand as Tsitsipas broke serve to lead 3-1.
After maintaining a higher first serve percentage and after hitting several forehand winners, Tsitsipas took second set leads of 4-1 and 5-2.
Djokovic held serve to reach 3-5 before Tsitsipas committed two groundstroke errors while serving at 15-30 to drop serve and reach 4-5.
The set then remained on serve to reach a tiebreaker.
In the tiebreaker, Tsitsipas struggled with his backhand as he committed three backhand errors to trail 2-3.
Djokovic then struck an ace down the tee to lead 4-2.
Another Tsitsipas backhand error sent Djokovic ahead 5-2.
Djokovic then struck a crosscourt backhand long which he followed up with two forehand errors to level the tiebreaker at 5 all.
Tsitsipas' one handed topspin backhand can be a spectacular shot.
However the Greek's backhand continued to be a source of disappointment for him in the tiebreaker as he struck two final backhand errors to close the match after one hour and thirty six minutes of play.
Djokovic, the reigning Roland Garros champion, improved his win-loss record this year to 12-4 with two final round tournament appearances.
On Friday in the quarterfinal round, Djokovic avoided losing his number one ranking to the second ranked Daniil Medvedev by defeating the eighth seeded Felix Auger-Alliseme 7-5, 7-6(7-1) in what would be his toughest match of the week.
Roland Garros also known as the French Open begins Sunday in Paris.