The defending champion eased past the up-and-coming American courtesy of a 6-1 6-2 6-3 win in a rapid 91 minutes.
Djokovic hit seven aces, getting 73 per cent of his first serves in, while producing an impressive 37 winners – and the world No1 will now meet Radek Stepanek in the next round on Friday.
“In the earlier rounds, yes, probably [one of my best Grand Slam matches],” said Djokovic.
“I’ve played many matches in Grand Slams in my career, so it’s tough to compare which one is the best I would take under the circumstances.
“And also it depends at what stage of the tournament and the quality of the player.”
Despite the emphatic victory, Djokovic insisted that he had to be at his best to beat Harrison, who is touted as a future Grand Slam winner.
“I definitely didn’t want to underestimate my opponent tonight, even though he’s younger than me, he still hasn’t established himself as a top 20 or top 30 player,” he added.
“But I still knew that he has a quality. Mentally he’s probably going to go out on the court knowing he doesn’t have anything to lose.
“He’s going to try to smack serves and forehands. I went with that kind of mindset on the court, you know, just trying to play as sharp as possible from the start, and I’ve done so.”
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BIOGRAPHY: Eric Bailly