Tsitsipas won the first set after erasing a set point in the tie-breaker with a difficult forehand winner. In the second set he looked fresher than the 34-year-old Djokovic,who was coming off an epic semi-final against Rafael Nadal.
But Djokovic steadied his game in the third set,which turned in the fourth game,when he converted his fifth break-point chance of the game.
After that,Tsitsipas appeared to lose his way,while Djokovic found his form.
During the changeover before the fourth set,Tsitsipas laid on his back and was stretched out by the trainer,a back injury apparently hindering his movement.
Fifth seed Tsitsipas appeared to be struggling physically but valiantly tried to dig in at the start of the fifth set as the shadows spread across a sun-lit Court Philippe Chatrier.
But Djokovic got the early break in the decider and although he was pushed hard,he was never threatened again.