The steely-eyed Serb warmed up with a workmanlike performance in his opener against Frenchman Paul-Henri Mathieu, but was at his devastating best in a 91-minute rout of the 62nd-ranked Harrison.
Bullied on the baseline and broken early in each set, the 20-year-old American scrambled hard to make a contest under the lights at Rod Laver Arena, but surrendered the match when his opponent ripped a searing forehand down the line.
Djokovic will continue his bid for a sixth Grand Slam title, and fourth at Melbourne Park, against Czech veteran Radek Stepanek, the 31st seed who beat Feliciano Lopez 6-2 6-2 6-4.
The world number one raced out of the blocks, moving 3-0 up with Harrison gifting him the second of those games with a double fault.
The American managed to hold to get on the board for 3-1, but was broken in his next service game while Djokovic was imperious on serve - despite the odd uncharacteristic hiccup - to take the first set.
A break at the start of the second stanza set Djokovic on his way - with the chance set up by a sublime looped topspin forehand lob on to the baseline - and the set followed a similar pattern with Harrison holding twice but being broken again in between times.
Harrison again lost a service game at the start of the third set, but rallied to take it to 5-3 before his renowned rival sealed the match with a forehand winner.
"You're trying to perform your best in every match that you play in and this was definitely a better performance than the first round," the 25-year-old said.
"I managed to play at a very high level already in the second round of a grand slam, which is very encouraging for the next challenge."
Number four seed David Ferrer survived a third-set wobble to move into the third round with a 6-0 7-5 4-6 6-3 victory over Tim Smyczek.
The Spaniard is 120 places ahead of Smyczek in the world rankings and for the first nine games of their clash on Margaret Court Arena it showed.
Ferrer raced through the first set 6-0 in 25 minutes and when he went 3-0 up in the second the crowd were already preparing for the next match due on court.
Then, Smyczek won his first game, let out an almighty "Yes!", and the chasm between their respective rankings suddenly narrowed. He was taking chances, making shots, getting more serves in - in his own words "taking it to" Ferrer.
The lucky loser, who beat giant Croat Ivo Karlovic in the first round, dropped the second set 7-5 but took the third 6-4 to get the crowd behind him.
Ferrer, Spain's main hope in the absence of Rafa Nadal, then kicked back into gear to take the tie 6-0 7-5 4-6 6-3 in two hours, 38 minutes.
The world number five responded, taking the fourth without too much fuss to book a third-round date with Marcos Baghdatis of Cyprus, after the 28th seed beat Japan's Tatsuma Ito 3-6 6-3 6-2 6-2.
Tomas Berdych was a man in a hurry as the fifth seed motored to a 6-2 6-2 6-4 win over Frenchman Guillaume Rufin in their second round match-up.
The Czech, a quarter-finalist in Melbourne the last two years, double-faulted when serving for the match to give Rufin a chance to break, but he recovered and sealed victory with an ace soon after.
Berdych will play Juergen Melzer of Austria for a place in the last 16, the 26th seed overcoming Spaniard Roberto Bautista Agut 6-7(4) 6-3 6-7(3) 6-3 6-2 in an epic contest.
Nicolas Almagro, the 10th seed, became the first man through to the third round after an early 6-4 6-1 6-2 victory over fellow Spaniard Daniel Gimeno-Traver. Almagro needed just an hour and 41 minutes to wrap up victory and he next meets Polish 24th seed Jerzy Janowicz, who recovered from an ugly on-court tantrum to beat Indian Somdev Devvarman 6-7 3-6 6-1 6-0 7-5.
The 24th seed exploded with rage over a line call in the tie-break at the end of the 79-minute first set, roaring his displeasure, hitting the umpire's chair with his racket and throwing his water bottle across court.
At one stage, the 22-year-old collapsed to his knees in frustration with his forehead touching the playing surface on court eight.
"I was really worried about his voice," said Indian Devvarman. "He was really yelling at the top of his lungs and I said, 'Dude, calm down'."
Devvarman took the tie-break 12-10 to win the set and, at the changeover, Janowicz again argued his case with Croatian umpire Marija Cicak before making the point more forcefully with his racket.
Despite tallying 88 unforced errors over the match, Janowicz regained his composure and was back on his knees in celebration 161 minutes later. The hour-long deciding set seeing the players exchanging service breaks before the Pole secured the victory with another blistering forehand return for his 91st winner of the match.
"The umpires, they're making so many mistakes ... this was the moment when I went nuts, otherwise the rest of the match I was pretty calm," said Janowicz, who reached the final of the Paris Masters last November.
"Sometimes it happens like this. You can't control your emotions all the time. This was a really big point for me. We played this set for more than an hour and 10 minutes, so this was a really important point for me."
American Brian Baker's hopes of a fairytale run at were ended in the cruellest of fashions when he was taken off court in a wheelchair after suffering a serious knee injury.
The 27-year-old, who returned in 2012 after seven injury-plagued years off the professional circuit, had won the first set of his second round match against compatriot Sam Querrey when he suffered the injury.
After receiving treatment on his right knee, Baker was wheeled away with a torn lateral meniscus, which will require surgery and four months on the sidelines.
"He's the last person that deserves anything like that with his five or six surgeries already," said Querrey.
Querrey, the sole American men's seed this year in the absence of injured compatriot John Isner, will now meet Swiss Stanislas Wawrinka for a place in the fourth round.
Janko Tipsarevic came through a epic five-set battle against Lukas Lacko 6-3 6-4 3-6 4-6 7-5.
The Serbian eighth seed took a two-set lead but the Slovakian recovered from a break down to win the third and make the crucial break in the fifth game of the fourth set as he took the match into a decider.
Having taken an injury time-out, Tipsarevic broke only for the world number 44 to break back, saving two match points in the process.
But Tipsarevic eventually completed the victory in nine minutes short of four hours and will face Julien Benneteau in round three.
Japanese trailblazer Kei Nishikori repelled Carlos Berlocq's baseline rockets and counter-punched his way to a 7-6 6-4 6-1 victory.
The slender 23-year-old, whose electrifying quarter-final run at last year's Australian Open made him the first Japanese man in the last eight at Melbourne Park in 80 years,
He withdrew with a knee injury when trailing by a set against Andy Murray in the semi-finals of the Brisbane International in the lead-up and has carried the complaint into Melbourne Park.
His knee was still taped against the Argentine journeyman and he strode gingerly off the court, but after taking an ice-bath the 18th-ranked Nishikori said he wasn't losing sleep over it.
"It's getting better and there's almost no pain. I just put tape there just in case," he said. "Everything is working well for me here."
He will face Evgeny Donskoy who defeated Russian compatriot and 23rd seed Mikhail Youzhny 3-6 7-6(4) 6-2 3-6 6-3.