The Serb, seeking a 25th Grand Slam to move past Margaret Court’s record of 24, won 7-6 (7-3) 4-6 6-2 6-3 in hot conditions to reach the semi-finals.
He will play on Friday against Italian fourth seed Jannik Sinner, who defeated Russian fifth seed Andrey Rublev.
“I suffered a lot in the first couple of sets,” top seed Djokovic, 36, said.
“I said [to my team] that this match was not an enjoyable match for me at all.
“It was really difficult to find the right timing. It was really hot while the sun was still out.
“We all know Taylor has got one of the best serves in the world. I knew the kind of threat he poses when he serves on such a high quality.”
Djokovic has won his past 33 singles matches at Melbourne Park and is a clear favourite to defend his title.
Sinner beat Rublev 6-4 7-6 (7-5) 6-3 in a match that finished at close to 01:30 local time on Wednesday morning after the start of the night session was pushed back to 21:00.
The singles matches on Rod Laver Arena did not start until 13:00. Coco Gauff’s win against Marta Kostyuk in the women’s quarter-finals took more than three hours before Djokovic needed almost four to beat Fritz, though Aryna Sabalenka made quick work of her 6-2 6-3 win over Barbora Krejcikova.