Women's 26th seed Elise Mertens was another winner, with the Belgian outlasting Spain's Garbine Muguruza, who was seen cramping before losing 3-6, 7-6 (7/3), 6-1.
Bianca Andreescu staged a dramatic comeback Sunday to topple Garbine Muguruza in a battle of former Grand Slam champions on day one of the Adelaide International
Top seed Djokovic brushed aside 79th-ranked Thanasi Kokkinakis of Australia 6-1, 6-4, 6-2 and will face Serbian compatriot Miomir Kecmanovic for a last-16 place
Wimbledon: Garbine Muguruza, 2017 Champion, Loses To Greet Minnen In Rd 1
Alize Cornet sent Garbine Muguruza crashing out of the Australian Open in the second round Thursday, upsetting the Spaniard 6-3, 6-3.
Australian Open: Muguruza carried that form on to Rod Laver Arena against 77th-ranked Frenchwoman Clara Burel, proving too powerful in winning 6-3, 6-4 in 88 minutes
World number three Garbine Muguruza said Saturday that the "real truth" about what happened to Peng Shuai may never be known after the tennis star accused a senior Chinese politician of sexual assault.
Muguruza will now play another Russian, Daria Kasatkina, in the quarter-finals after she upset Belgian Elise Mertens 6-3, 6-4.
Nick Kyrgios and former world number one Andy Murray will play in the Sydney Tennis Classic, which begins on January 10, ahead of the Australian Open.
Garbine Muguruza beat Anett Kontaveit 6-3, 7-5 on Wednesday to become the first Spaniard to win the elite season-ending WTA Finals in Guadalajara, Mexico.