The 35-year-old Mannarino had gone to five sets in all three of his previous rounds. After missing a break point in the opening game, he almost never threatened Djokovic.
The Frenchman avoided a so-called triple-bagel – only five Grand Slam matches in the Open era have been won 6-0, 6-0, 6-0 – but he was only postponing the inevitable.
Djokovic has admitted to feeling unwell in recent rounds but said his health is improving.
“[The] last couple of days have been really good,” he said. “It’s going in a positive direction, health-wise, tennis-wise.”
Djokovic plays 12th-ranked Taylor Fritz, who beat No 7 Stefanos Tsitsipas, the runner-up here last year, in four sets.
Defending champion Aryna Sabalenka and US Open winner Coco Gauff cruised into the women’s quarter-finals with commanding wins.
No 2-ranked Sabalenka, who won her first Slam title in Melbourne last year, beat Amanada Anisimova 6-3, 6-2. Gauff, who picked up her first major at the US Open in September, beat Magdalena Frech 6-1, 6-2.
Anisimova had won four of their previous five meetings but she didn’t have the answers this time to counter the power of the Belarusian, who hit 18 winners.
“I’m super happy with the level, happy to get this win, she’s a tough opponent,” Sabalenka said. “I love the atmosphere here, I love playing in front of you guys. I really want to stay as long as possible and hopefully, we can get this thing one more time.”
A brief rain delay at 4-1 in the first set stopped Sabalenka’s momentum but she quickly recovered and pulled away in the second set. She’ll meet either 16-year-old Mirra Andreeva or No 9 Barbora Krejcikova in the last eight.
Gauff was the first woman through, needing just 63 minutes to see off Frech in a match played on Rod Laver Arena — in front of the Australian great.
“Luckily when I saw him come in I was already well up,” Gauff said. “I heard clapping and knew it wasn’t for us, it was only the first set. But thank you for coming, it’s an honor.”
Gauff will play Marta Kostyuk after the Ukrainian beat Maria Tomafeeva 6-2, 6-1 to reach the major quarterfinals for the first time.
Still a teenager, Gauff drew attention to her shoes, which carry a number of messages, including one that says: ‘you can change the world with your racket,’ something her father told her as a little girl.