Djokovic produced an impressive all-round display in seeing off his opponent 6-4 6-2 6-2 in less than two hours, setting up a meeting with Kei Nishikori for a place in the final four.
After dropping the opening serve of the contest, the Serbian broke right back and quickly found his stride, going on to win 51% of the points on Khachanov's serve.
The former world number one lost his serve in the seventh game, too, but Khachanov simply could not take advantage and Djokovic made no mistake by claiming his first set point when it arrived.
Djokovic, who will be competing in his 41st Grand Slam quarter, had far more joy in the second and third sets as he held throughout.
A long rally culminated in Khachanov guiding a backhand into the net for his opponent to claim match point at the third attempt.