The world number one raced into a 3-0 lead in the first set, his pace proving too much for Harrison early on.
The American did manage to get a game on the board after that but Djokovic remained in complete control, pushing his opponent to all corners of the court on every point.
Harrison tried to mix up his play, even trying to serve-volley, but it made no difference as he had no answer to Djokovic's power and precision. The defending champion comfortably served out the set for 6-1.
Djokovic signalled his intention to get the match over as quickly as possible with a break in the opening game of the second set.
Some powerful serving helped Harrison get back to 2-1 but Djokovic went up a gear, making some incredible shots look routine from both the net and the baseline.
Harrison did manage one more game, before Djokovic found a tight angle to make a cross-court forehand and take the second set 6-2.
The third set started in similar fashion to the previous two, with Djokovic breaking his opponent. This time though, Harrison managed to stay with the world number one, winning his serve consistently after that.
That was until the ninth game of the set, when Djokovic produced a monster forehand to break the 20-year-old and win the match.
Djokovic will face Radek Stepanek in the third round.