Djokovic beat the 23-year-old German 6-7, 6-2, 6-4, 7-6 in just over three and a half hours.
Nursing an abdominal strain, it was a success born of grit and fortitude rather than the Serb's trademark dazzle.
"With this injury, I need time to warm up and actually feel like I can rotate well," he said after the win on Rod Laver Arena.
"I started moving better and playing better. I served extremely well and I think I had slightly more aces than him, which for me is a miracle.
"I kind of regained my focus after I broke that racquet and things started to shift to me in a positive direction."
Record
Djokovic, who is seeking a record-extending ninth Australian Open title, last tasted defeat at the tournament in the fourth round in 2018, when he was upset by the unseeded Hyeon Chung.
The 33-year-old - hunting an 18th Grand Slam title - will be the favorite to advance to Sunday's final when he plays the Russian qualifier Aslan Karatsev.
The 27-year-old continued his dream run with a 2-6, 6-4, 6-1, 6-2 win over the 18th seed Grigor Dimitrov.
"I hadn't seen him play before the Australian Open," Djokovic said of Karatsev who is 113 places below him in the rankings.
"He's very physically strong and moves well. He has a lot of firepower from the back of the court. He's motivated and has nothing to lose."
