The 17-time Grand Slam champion was never in any trouble against the 35th-ranked Ukrainian and strolled to a regulation 6-3, 7-5, 6-1 win in one hour 33 minutes on Rod Laver Arena.
It was 34-year-old Federer's 299th Grand Slam singles victory as he chases his fifth Australian crown.
Federer, world number three, practised with the pony-tailed Dolgopolov in Dubai in the off-season and took his record over him to 3-0.
Dolgopolov's game unravelled in the final set as the Swiss maestro put the finishing touches to a convincing win.
The third seed, who has now reached the third round in all of his 17 visits to Melbourne, broke Dolgopolov's serve five times and did not face a single break point on his own serve.
The Swiss legend hammered a total of 39 winners, which included 25 aces in a dominant serving performance.
Federer will now have a third-round encounter with either Bulgarian 27th seed Grigor Dimitrov or Argentina's Marco Trungelliti.
“I'm very happy,” Federer said. The conditions are extremely quick so you are not going to find that much rhythm out there,” Federer said.
“Aleksandr can play great when you give him too much time so maybe it wasn't a bad thing that it was as fast as it was.
“But I served well and as the match went on I started to feel better and better, but the second set was crucial and I'm glad I got it done.”
ROGER FEDERER
Federer cruises to win against practice partner
Basel native Roger Federer cruised into the Australian Open third round with a smooth, straight-sets win over practice partner Aleksandr Dolgopolov on Wednesday.
ROGER FEDERER
Is this the end of the road for Swiss tennis legend Roger Federer?
Roger Federer is talking optimistically about returning to his "highest level" after knee surgery, but does tennis have to start adjusting to a future without the Swiss star?
The 20-time Grand Slam winner announced on Wednesday that he would be sidelined until 2021 after his second operation in a matter of months.
Federer remains upbeat, tweeting: “I plan to take the necessary time to be 100 percent ready to play at my highest level.”
In some ways 2020 is a good season to miss after the coronavirus ravaged the tennis schedule. Writing Federer off in the past has proved dangerous.
He returned from a six-month injury lay-off to claim the Australian Open in 2017, winning his eighth Wimbledon crown later that year.
But he will be 40 in 2021 and is now heading into uncharted territory.
Despite his groaning trophy cabinet, there are two factors that will motivate Federer to keep going — the risk of losing his grip on the men's Grand Slam title record and a missing Olympics singles gold medal.
Rafael Nadal has 19 majors, just one shy of Federer's mark and Djokovic has 17.
Spain's Nadal will be fancied to draw level with Federer at the French Open, rescheduled for September, while few would bet against Djokovic winning in New York weeks earlier.
In April, Federer said he was “devastated” when Wimbledon was cancelled for the first time since World War II. Last year he fell agonisingly short at the All England Club, failing to convert two championship points on his own serve against Djokovic.
The Wimbledon grass probably remains his best chance of adding to his Grand Slam collection — he has not won the US Open since 2008 and his only title at Roland Garros came in 2009.
Even though Federer has slipped from the very pinnacle of the game, he is still a major threat to Nadal and Djokovic.
'Golden' ambitions
Last year, the world number four had a 53-10 win-loss record and he reached the semi-finals at the Australian Open in January in his only tournament this year.
Federer, who is still six ATP titles short of Jimmy Connors' all-time record of 109, has one glaring omission from his CV — the Olympic title.
The Swiss won doubles gold in Beijing in 2008 with compatriot Stan Wawrinka but lost in the singles final to Andy Murray in London four years later.
The postponed Tokyo Games will almost certainly be Federer's last opportunity to complete a career “golden” Grand Slam — he will turn 40 on the day of the closing ceremony next year.
Tennis will feel the loss of the elegant Federer keenly when he walks off the court for the last time.
Djokovic and Nadal have been the dominant forces in recent years but the Swiss remains the biggest draw and last month topped Forbes' list of the world's highest-earning athletes.
His last appearance on court was in front of nearly 52,000 fans — touted by organisers as a world record for tennis — at a charity match against Nadal in Cape Town in February.
Federer is nearly always the crowd favourite wherever he plays and has proved a perfect ambassador for the sport since he won his first Grand Slam title in 2003.
He certainly expects to be back and competitive next year.
“I will be missing my fans and the tour dearly but I will look forward to seeing everyone back on tour at the start of the 2021 season,” he tweeted.
The avalanche of support from his adoring fans showed they would miss him too, but they will have to get used to a time when he is gone for good.
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