He now owns the record for playing the most consecutive Grand Slam events, another milestone in a career that has already netted 17 major titles for the Swiss star.
He kept the points as short as possible, giving No 133-ranked Duckworth only one look at a break point in the one-hour, 46-minute match.
Federer said it was "great fun" to finally play in front of childhood hero Edberg, whom he hired on a part-time basis last month.
"I used to watch his matches and get inspired," Federer said, then added: "He warmed me up ... I won!"
No 11 Simona Halep won 6-0, 6-1 over Polish qualifier Katarzyna Piter, while American Christina McHale advanced 7-5, 6-4 over Taiwan's Chang Yung-jan and No 16 Carla Suarez Navarro of Spain beat Vania King of the United States 6-3, 6-2.
Players draped bags of ice over their necks and shoulders and sat under covered seats in the changeovers across Melbourne Park. They retreated into the shade at the back of the courts between points.
A hot, gusty breeze swirled across the venue all day, making conditions more challenging instead of cooler. Spectators on outside courts covered their heads and shoulders with damp towels to cool off and queued up to stand in front of large electric fans blasting water at their faces.
As well as the heat, there were injuries and retirements. Heineken Open winner John Isner, the only seeded American man in the draw, retired after losing the first two sets 6-2, 7-6 (6) against Martin Klizan.
Isner attributed his exit to the right ankle problem that bothered him on the way to last week's Auckland title.
It was the second retirement in as many matches on Court 6. No 25 Alize Cornet had to win only one game before Polona Hercog of Slovenia retired with an undisclosed injury.
Philipp Kohlschreiber of Germany didn't make it on to court, withdrawing before his first-round match because of a strained left hamstring.
The No 21 seed was replaced in the draw by Frenchman Stephane Robert, who beat Slovenia's Aljaz Bedene 7-6 (3), 6-3, 6-0.
Among the other men advancing were No 10 Jo-Wilfried Tsonga, No 11 Milos Raonic, No 22 Grigor Dimitrov and No 16 Kei Nishikori, who beat Australian Marinko Matosevic.
- AP
