Quentin Halys, a 19-year-old wild card, has been a fixture on the lower-level circuits and was once the No. 3-ranked junior in the world.
Predictably, Djokovic beat his overmatched opponent 6-1, 6-2, 7-6 (3) to reach the third round for the 10th straight season.
After cruising early, Djokovic faced a momentary lapse early in the third when he was broken by the 187th-ranked Halys. The Serb recouped quickly, but his younger opponent maintained his level and sent the set into a tiebreaker.
After an 11-shot opening rally that ended with Halys hitting a spectacular one-handed slice backhand around the net post for a winner, Djokovic pulled away.
"He's new on the tour, but today he played some great tennis," Djokovic said of his opponent. "I just want to congratulate him for fighting, and I wish him the best."
Despite the straight-sets affair, the match was separated by only one break until late in the second. Not surprisingly, the difference in the match was Federer's precision-like serve. He finished with 25 aces and won a whopping 88 percent off his first deliveries.
"I thought today I did serve very well," Federer said. "You know, maybe just matched up well with Dolgopolov. Maybe he wasn't seeing [the ball] as well. But also conditions are fast during the daytime, so that helps to be able to serve through opponents.
"I'm happy I got crucial first break in the first set. I think it was a big set for me. Then second set was the key, really, because it was close for a while. I had missed some chances. I was keeping it up, you know, serving well, keeping the pressure on, and finally then found the break end of the second."
As for Djokovic, the last time he lost to a player ranked as low as Halys came six years ago in Belgrade when he retired against No. 319 Filip Krajinovic.
Djokovic is looking to extend his Open era record of five Aussie Open titles. Last year, he beat Andy Murray in the final and then went on to win Wimbledon and the US Open. If not for an inspired Stan Wawrinka in the final of the French Open, Djokovic would have become the first player since Rod Laver in 1969 to sweep all four majors.
"This court gives me so many beautiful memories," Djokovic said. "This is the first Slam I won in 2008, and every time I step onto Rod Laver, it feels so special.
No. 6 Tomas Berdych dominated Mirza Basic, a qualifier from Bosnia, 6-4, 6-0, 6-3. Berdych belted 43 winners in the 1-hour, 38-minute encounter to reach the third round for the sixth straight year. Last season, Berdych matched his best Australian Open performance by reaching the semifinals. He beat Nadal en route to the final four, thus ending a 17-match losing streak against the Spaniard.
Thiem, 22, is widely recognized as one of the game's brightest future stars. He defeated former world No. 9 Nicolas Almagro 6-3, 6-1, 6-3. Thiem was helped by his Spanish opponent's sloppy play. Almagro donated 49 unforced errors and didn't have a single break opportunity.