The world number one was in irresistible form, outclassing the young American 6-1, 6-2, 6-3 in just 1hr 31min of high-class tennis on Rod Laver Arena.
Djokovic, a three-time winner and going for three straight Australian titles, will next play Czech journeyman Radek Stepanek in the last 32.
"I tried to focus on the start and I knew that he had nothing to lose and would come out with his big serves, but I managed to make some very important early breaks at the start of the match," Djokovic said.
"I was a set up after 20 minutes and it was a mental advantage, I felt much more comfortable on the court.
"I don't think he was playing at his best, it was probably the occasion playing on the centre court, but I wish him all the best, I think he has a good future."
Djokovic jumped out of the blocks and won 12 of the first 13 points to put the young American on the back foot and down an early service break.
He broke Harrison again in the sixth game and wrapped up the opening set in just 20 minutes.
The Serb top seed carried on where he left off breaking the American's opening service to win seven of the first eight games.
Djokovic broke Harrison's serve for a fourth time to carry on the blitz and raced to a two sets to love lead via three set points in 30 minutes.
Harrison was broken again in the opening game of the final set as Djokovic closed in on victory.
But the young American refused to give in and held three service games under pressure, to the appreciation of the centre court crowd.
Djokovic again put Harrison's service under pressure and took out the match on his second match point.
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