Djokovic is never at his most comfortable in windy conditions but he made a flying start against Japan's Tatsuma Ito and dropped just seven games in a 6-1 6-4 6-2 victory.
The second set was tight but, once the defending champion took that, any semblance of danger passed.
Djokovic said with a smile: "I was like, 'Yes, it's going to be a windy day. I love the wind.' I'm being sarcastic now, of course.
"I don't think players enjoy these kind of conditions. You have to accept them and embrace the fact that I guess you're going to be challenged on different levels, not just by your opponent, but also the conditions.
"That's OK. I accepted it. I came into the match and played extremely well at the beginning. Got a 5-0 lead up after 15 minutes. I'm just overall pleased with the performance."
Djokovic, who next plays another Japanese in Yoshihito Nishioka, hit 16 aces and won 43 of 46 points when he landed his first serve.
"My serve was working extremely well in the first round and second round," he said.
"That's something I worked on in the off-season. That's one of the priorities I guess of the training sessions, trying to get that advantage of winning a lot of easy points on the first serve. It has been paying off so far I think in ATP Cup and here."
Federer went one better than Djokovic in a 6-1 6-4 6-1 victory over Serbian Filip Krajinovic.
The third seed admitted he felt a little sorry for his opponent, who played a five-set first-round encounter on Tuesday having been rained off on Monday while Federer played indoors.
The third seed said he had low expectations coming into the tournament having not played a competitive match since November but he has been very sharp so far and maintained his record of always having reached at least the third round on each of his 21 visits to Melbourne Park.
In the third round, the Swiss will take on popular Australian John Millman, who he lost to in very hot and humid conditions at the US Open in 2018.
Federer remembers it as the worst he has felt physically after a match, saying: "I don't know anything remotely close. I was just happy it was over. I never had that.
"I think the next match is really going to be a test for me because John is going to be there. He's fit like a fiddle. He's from this country, so naturally also it's going to be different intensity."
Their New York meeting is a special memory for Millman, who said: "The way I see it is, you take a few snapshots, you have a few of those memorable moments that hopefully when you finish playing tennis you can think back and think that was pretty cool. That was one of those moments.
"I'll go out there and leave it all out there. If lightning strikes twice, I wouldn't say no to it. It's what you want to do. Home slam against someone like Roger, it's pretty cool."
Sixth seed Stefanos Tsitsipas did not even have to take to the court, with German opponent Philipp Kohlschreiber withdrawing because of a muscle strain.
The first top-eight seed fell, Italy's Matteo Berrettini recovering from two sets down against 2018 quarter-finalist Tennys Sandgren only to lose 7-6 (7) 6-4 4-6 2-6 7-5.
Grigor Dimitrov experienced a similar fate against young American Tommy Paul. He looked poised to dig himself out of a deep hole when he served for the match in the fifth set but 22-year-old Paul claimed the biggest victory of his career, winning 6-4 7-6 (6) 3-6 6-7 (3) 7-6 (3).
Exciting 18-year-old Jannik Sinner was unable to make it past the second round, going down 6-4 6-4 6-3 to Denis Shapovalov's conqueror Marton Fucsovics, but there were wins for Roberto Bautista Agut, Milos Raonic, Marin Cilic and Diego Schwartzman.