His reward is a meeting with Canadian Milos Raonic in the next round, against whom he boasts a 4-0 record.
Luxembourgian Muller started the season strongly, making the semi-finals at the Sydney International and he had beaten two Australian Open seeds on his way to the fourth round.
But the step up in class was always going to challenge the 31-year-old, who won just 23 of his 74 baseline rallies.
Muller was able to compete well off his serve and at the net, forcing Djokovic to wait patiently for his break opportunities.
Djokovic earned a decisive break in the first set at 3-3, and again in the second set at 5-5 with a tiebreak looming.
Muller lifted his all-around performance in the third set, forcing the world No.1 to rally for longer.
He earned his first break points of the match at 2-3 in the third set and with them a glimmer a hope.
But the left-hander missed his four opportunities and with it a chance to find a foothold into the contest.
With the crowd firmly behind the four-time Australian Open champion, he finally broke through at 5-5 and served truly to enter the last eight just before midnight on Australia Day.
The victory was Djokovic's fourth straight win during this campaign without a drop of set - and remarkably just one break of serve to date.
- AAP