Six-time champion Djokovic, chasing his third Grand Slam title in a row, cruised past American qualifier Mitchell Krueger 6-3 6-2 6-2 at the Rod Laver Arena.
The 31-year-old Serb has been in sparkling form since recovering from elbow surgery last year, winning Wimbledon and the U.S. Open to regain the world number one ranking.
"It feels great to be healthy and back on this court again," said Djokovic, who was appearing in his 300th Grand Slam match.
"Twelve months ago it was quite a different sensation on the court with the elbow injury. Twelve months forward, obviously things are quite different."
Halep roared back to conquer Kaia Kanepi 6-7(2) 6-4 6-2, avenging her US Open opening round defeat by the Estonian veteran last year.
The 27-year-old Romanian will next face American Sofia Kenin, who arrived in Melbourne after clinching her maiden WTA title at the Hobart International last week.
Serena Williams, chasing a record 24th Grand Slam title in the Open Era, started her campaign with an impressive 6-0 6-2 win over German Tatjana Maria.
The 37-year-old American, whose 23rd major title came in Melbourne when she was pregnant two years ago, peppered the court with her heavy groundstrokes to seal the victory in just 49 minutes.
Serena's older sister Venus had to work harder for her 6-7(3) 7-6(3) 6-2 win over Romanian Mihaela Buzarnescu.
An injury-hampered Nick Kyrgios suffered his earliest exit from his home Grand Slam when he was beaten by Canadian power-hitter Milos Raonic 6-4 7-6(5) 6-4.
