It's been three and a half years since the 34-year-old Federer won the most recent of his record 17 grand slam titles at Wimbledon, although he remains hopeful of adding to the tally.
"A lot of retired players could still be at this level too - they just choose not to do it anymore," the 34-year-old said.
"It's all in the mind, the body, it's the family and the travelling, so many things that are a part of this whole thing.
"It's been going very well for me and I hope to keep it up as long as I choose to play tennis.
"But there's always a danger.
"Like last year here the third round was the end for me (when he was dumped out of the tournament by Italian Andreas Seppi), so I hope to go further this time."
The key moment came in the 11th game of the second set when Dolgopolov made a hash of an ill-advised drop shot, opening the door for Federer to break for 6-5.
"The conditions are extremely quick so you're not going to find that much rhythm," said Federer, who has won four Australian Open crowns.
"I thought I served great.
"As the match went on I felt better and better, but the second set was clearly crucial."
A host of other leading men's seeds joined Federer in marching into the round of 32 on Wednesday.
No.6 Tomas Berdych was untroubled in ousting Bosnian qualifier Mirza Basic 6-4 6-0 6-3.
The Czech has reached the semis at Melbourne Park in each of the past two years, but he'll need to beat Australian firebrand Nick Kyrgios to get there this year.
Kyrgios was largely untroubled in defeating Pablo Cuevas 6-4 7-5 7-6 (7-2).
Kei Nishikori also eased into the round of 32 with a straight-sets win over American Austin Krajicek.
The No.7 seed eclipsed his long-time friend and training partner 6-3 7-6 (7-5) 6-3.
Nishikori's best result at Melbourne Park is the quarter-finals, which he reached in 2012 and 2015.
Popular Frenchman Jo-Wilfried Tsonga dispatched Melburnian teenager Omar Jasika 7-5 6-1 6-4 and will play countryman Pierre-Hugues Herbert on Friday.
Belgian 15th seed David Goffin is also through to the third round but not before suffering the indignity of a bagel in the second set against Bosnian Damir Dzumhur.
But Goffin recovered quickly, going on to win 6-4 0-6 6-4 6-2.
His third-round opponent will be Austrian 19th seed Dominic Thiem, who trounced Spaniard Nicolas Almagro 6-3 6-1 6-3.
No.12 seed Marin Cilic from Croatia downed Spaniard Albert Ramos 6-4 6-3 7-6 (7-4).
- AAP
