Defending champion Federer beat Aljaz Bedene 6-3, 6-4, 6-3 in a night match, his first on Rod Laver Arena since clinching a career-reviving title here last year.
Federer has been met on court after wins here previously by tennis greats Laver, John McEnroe and Jim Courier.
On Tuesday night, he got something different. Comedian Will Ferrell stepped out of the crowd and, slipping into character as Ron Burgundy from the movie "Anchorman," conducted the postmatch interview.
Six-time champion Djokovic and 2014 Australian Open winner Stan Wawrinka stuck to business, returning from long injury layoffs with victories in their first matches since Wimbledon.
Djokovic tweaked his service motion while recovering from an injured right elbow and used it to good effect in a 6-1, 6-2, 6-4 win over Donald Young.
Djokovic lost in the second round here last year but won five of the previous six Australian Open titles.
"Obviously I wanted to start with the right intensity, which I have," Djokovic said. "I played perfect tennis, like I never stopped."
Wawrinka, who had six months out after surgery on his left knee, beat Ricardas Berankis 6-3, 6-4, 2-6, 7-6 (2).
The 2014 champion connected on only 50 percent of his first serves and was broken four times in the match. He also looked physically spent toward the end of the fourth set before rallying to dominate the tiebreaker and close out the match.
Wawrinka underwent surgery on his left knee after Wimbledon and didn't play another match in 2017. He delayed his comeback at the start of this season by pulling out of a couple of exhibitions before the Australian Open and made a last-minute decision to take part in the tournament.
"I'm proud to be back already," he said after his match. "Honestly, to win today, it means a lot for me."
The ninth-seeded Swiss player is also playing without a coach after splitting with longtime coach Magnus Norman in October.
No. 4-ranked Alexander Zverev and No. 7 David Goffin advanced, but No. 20 Roberto Bautista Agut lost to Fernando Verdasco, a semifinalist here in 2009, and former Wimbledon finalist Milos Raonic lost 6-7 (5), 7-5, 6-4, 7-6 (4) to Lukas Lacko.
Information from The Associated Press was used in this report.