The 10-time champion needed four sets to progress in each of his first two matches, against Dino Prizmic and Alexei Popyrin, but was never in trouble against the Argentine, cruising to a 6-3, 6-3, 7-6(2) win.
"It was a great match, I think the best performance I have had during this tournament and I'm pleased with the way I played throughout the entire match," he said as cheers rang out on Rod Laver Arena.
The world number one has been under the weather in Melbourne, regularly blowing his nose during changeovers, and admitted he has not been at his best.
But there was no drama in the Friday evening match on centre court as the Serb produced a trademark-focused performance full of control.
He did not face a single break point in the match, which lasted just under two-and-a-half hours.
Djokovic, chasing a historic 25th Grand Slam title, which would break his tie with Margaret Court, drew first blood when he broke in the sixth game of the first set for a 4-2 lead and he closed out the set.
He was quickly back on the attack in the second set, breaking for a 2-1 lead against his opponent, who ousted Andy Murray and Gael Monfils from the tournament, and he broke again to take the set.
Etcheverry dug deep in the third set and took it to a tie-break but there was a sense of inevitability about the outcome, with Djokovic firing an ace to seal victory in style.
The top seed has reached a century of appearances at his most successful major and is now behind only Roger Federer (117) and Serena Williams (105).
Djokovic will face either French 20th seed Adrian Mannarino or American 16th seed Ben Shelton in the last 16.
