The Serb world number one was too strong for unseeded Gilles Muller of Luxembourg, winning 6-4, 7-5, 7-5 in the night match on Rod Laver Arena.
The four-time champion did not have his service broken as he powered through to play Canada's Milos Raonic for a place in the semi-finals.
Djokovic was outstanding on service, winning a high 82 percent of first serves and fighting off four break points.
The Serb top seed hit 47 winners and only 16 unforced errors in a masterly performance against the left-handed Muller.
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"I was fortunate to serve very well in important moments in the third set and not allow him to capitalise on his break point opportunities."
Raonic became the first Canadian man to reach the Australian Open quarter-finals in 47 years in a five-set battle with Feliciano Lopez.
The eighth seed thundered down 30 aces as he made the last eight with a 6-4, 4-6, 6-3, 6-7 (7/9) 6-3 win over the 12th-seed in 3hr5min on Hisense Arena.
He also equalled countryman Robert Powell's feat of playing in three Grand Slam quarter-finals set back at the 1908, 1910 and 1912 Wimbledons.