In his 23rd consecutive Grand Slam quarter-final, Djokovic will face Milos Raonic for the fifth time. Djokovic leads 4-0 in their career meetings and has only lost one set against the Canadian.
Djokovic is yet to drop a set at Melbourne Park as he looks to become the second man in history to win the Australian Open for the fifth time.
He won his maiden Grand Slam championship here in 2008, before winning three successive titles from 2011-13. He is through to the quarter-finals for the eighth year in a row and will hope to make up for the five-set defeat he suffered to Stan Wawrinka at this stage last year.
As Australia Day came to a close, Djokovic came up against stern resistance from the 31-year-old Muller, now coached by Briton Jamie Delgado.
The resurgent Muller was playing in the fourth round of a major for the first time since the 2011 US Open after upsetting 13th seed Roberto Bautista Agut in the second round and the 19th seeded John Isner in the third round.
The Serb limited the big-serving Muller to just two aces in the 32-minute opener. He broke for a 4-3 lead before closing out the set, with his momentum halted only briefly as he had his grazed fingers - hurt as he put a hand on the court to steady himself - treated by the physio.
Muller managed to keep Djokovic at bay for much of the second set. He fended off three break points before the Belgrade native made a decisive move, breaking for a 6-5 lead and taking charge of the contest.
Djokovic wavered at times in the third set, but did just enough to close out Muller. He saved three break points for Muller in the seventh game before finally converting his fifth opportunity of the set to break Muller in the 11th game, claiming victory in two hours and eight minutes.