Fifth seed Dominic Thiem, 24, recovered from two sets down to beat American Denis Kudla and reach the last 32.
The second seed Federer saw off Struff 6-4 6-4 7-6 (7-4) and will play French 29th seed Richard Gasquet in the third round.
Lleyton Hewitt and Sam Groth pulled off a minor tennis miracle by knocking out the third seeded pairing of Horia Tecau and Jean-Julien Rojer in the second round of the men's doubles draw.
Federer who is worth approximately $420 million (£304 million) will earn £2.32 million if he wins the Australian Open tournament this year, which will mean his 20th Grand Slam.
Is a repeat of 2017 on the cards?
I'm really pleased with where my game is at at the moment.
But Chung, who defeated Russian Andrey Rublev to claim his first title at the Next Gen ATP finals in Milan last year, levelled the set scores with a tiebreaker win after holding three set points when the German netted a forehand.
Dominant in the first set, the going only got tougher from there for Federer.
The third set followed a similar pattern as Gasquet tried desperately to keep pace.
"I just think it's important to sometimes take a step back and actually see the good things you've done, give yourself time, maybe set the bar a bit lower".
Roger Federer cruised through the first set 6-2 against Richard Gasquet.
The 21 year-old Korean is another promising youngster, who will now face Djokovic after the Serb came through in straight sets against the No 21 seed, Albert Ramos-Vinolas, who was capable of winning only eight games. I could have gone on for a lot longer, but I could tell [John] McEnroe gave me the look, wrap it up. Gasquet was distraught, certain it was wide. "I run around the backhand presently", he said.
Del Potro, the 2009 U.S. Open champion, had made it to the final in Auckland a week before this year's Australian Open, losing to Roberto Bautista Agut.
"I wouldn't have minded playing during the day - I hope I survive under those conditions too", he said. "We both played a good level", he said, "so it was fun". I remember I had a hurdle to pass the quarters.
Djokovic urged tennis organizers to be more flexible about the rules for drink breaks, time between points and suspension of play when the conditions were bordering on dangerous.