Federer returned to stadium court on Sunday afternoon and needed an hour to finish off his second round victory 6-3, 7-6 (8/6).
Reflecting on the match, Federer said that he played an aggressive form of tennis at the same time also mixing up his game nicely with drop shots.
Federer will face 25th-seed Filip Krajinovic in the third round. He is making a cautious return after an right elbow injury in 2017.
"So talking about faster, I just think there is more bounce to it, especially if you play someone who has a lot of spin like he has and kicks the ball around a lot". She played here as a wild card a year ago as well and was eliminated early by Monica Puig, but financial support from Oracle - whose boss, Larry Ellison, also owns this tournament - has given her career a boost.
"I just completely lost rhythm, everything", Djokovic told reporters afterwards. "Very weird", Djokovic said.
Djokovic had four aces but overall he served poorly making four double faults and winning just 65 percent of his first-serve points.
The Melbourne event was Djokovic's first since Wimbledon last summer, as he was sidelined due to the elbow ailment that ultimately led to the operation. "When you go away from the game for over a two-month period, it starts feeling a little bit that way", the Express quoted Federer as saying.
Chardy, who came into the all-French tussle with an unbeaten record against Mannarino from their three previous meetings, edged the opening set before the French No 2 hit back to force a decider and claim his first set against the 31-year-old.
Frenchman Gael Monfils survived a match point before beating big-serving American John Isner 6-7 (5) 7-6 (3) 7-5 in a contest that had only one break.
Federer, who took over from Rafael Nadal as the top ranked ATP men's singles player in February, needs to make, at least, the semi-finals in order to remain at the summit.
Other seeded players who lost were ninth-seeded Lucas Pouille, who fell 6-4, 6-4 to Yuki Bhambri; 14th-seeded Diego Schwartzman, 7-5, 6-4 to Marcos Baghdatis; 21st-seeded Kyle Edmund, 6-4, 6-4 to Dudi Sela; and number 24 seed Giles Muller, 6-3, 7-5 to Pierre-Hugues Herbert.