With his 102nd match victory at Melbourne, the evergreen Serb equalled six-times champion Roger Federer's record at the year's first major and also became the first player to secure 400 wins at the Grand Slams.
"I feel really good. It's been a great start," the 10-times Melbourne Park champion declared.
"Things can change and I'm not getting ahead of myself, because last year I learned a lesson, I got too excited too early in some of the Slams, playing well and getting to the quarter-finals and semi-finals and then getting injured.
"I'm still trying to give these young guys a push for their money. I'm still around and hanging in there. Carlos Alcaraz and Jannik Sinner are playing at a different level.
"But when you enter the court and the ball rolls, you always have a chance ... especially on this court. I look forward to a good battle."
Djokovic opened the evening session on a steamy day in which play continued under the main showcourt roofs and eased to a 5-3 lead before firing a sublime backhand crosscourt winner and celebrating with his arms out to mimic an airplane.
He endured minor turbulence following that point, but had no trouble taking full flight again as he broke in the opening game of the second set when a deflated Van de Zandschulp fired his backhand long.
Djokovic briefly lost his cool while up 4-2, striking a ball that flew close to a ball kid stationed near the net. Though the Serb avoided a code violation, the incident triggered memories of his 2020 US Open default for striking a line judge.
Up two sets, Djokovic had treatment for a blister on his right foot after a tumble in the third and rallied from a break down before holding his nerve in the tiebreak to set up a clash with either 16th seed Jakub Mensik or Ethan Quinn.
"A few points before (I fell) I almost twisted my ankle and wanted to see the physio for my blisters," Djokovic said.
"Thankfully, I managed to have a good fall and protected myself. Things could have been very ugly in that moment."