The seventh seed met Stanford University graduate American Nishesh Basavareddy (ATP 107) and suffered a loss in the first set, but was superior in the next three, winning 4-6, 6-3, 6-4, 6-2.
Djokovic is fighting for his 25th Grand Slam title and 11th at the Australian Open in Melbourne.
In November, Djokovic approached Murray, one of his former rivals, and the British tennis player agreed to work as his coach.
In three sets, the first racket of the planet, the Italian Yannick Sinner, overcame the Chilean Nicolas Jarry (ATP 36) 7-6 (7:2), 7-6 (7:5), 6-1. Quick victory also for the owner of the third position, the Spanish Carlos Alcaraz, who defeated the Kazakh tennis player Alexander Shevchenko (ATP 77) with 6-1, 7-5, 6-2.
The currently unranked Australian Nik Kiris experienced failure. The former number 11, who is struggling with wrist and knee problems, lost to British Jacob Fearnley (ATP 92) 6-7 (3:7), 3-6, 6-7 (2:7).
The tournament also ended for 2023 finalist Stefan Tsitsipas – the 12th-ranked Greek lost to American Alex Mikkelsen (ATP 42) 5-7, 3-6, 6-2, 4-6.
The Australian Open Championship, which is the first “Grand Slam” tournament of the season, will run until January 26