The 32-year-old, chasing a 17th Grand Slam and eighth Australian Open, won 6-1 6-4 6-2 in one hour and 35 minutes.
The Serb now faces Japan’s Yoshihito Nishioka after he knocked out British number one Dan Evans in straight sets.
Italian eighth seed Matteo Berrettini became the highest-ranked player to exit, losing to Tennys Sandgren.
After losing the first two sets, it had looked like a comeback was on the cards when Berrettini took the match to a fifth set. But American world number 100 Sandgren went on to win 7-6 (9-7) 6-4 4-6 2-6 7-5.
Meanwhile, sixth seed Stefanos Tsitsipas did not even have to hit a ball as he reached the last 32 after opponent Philipp Kohlschreiber withdrew injured.
Organisers said the 36-year-old German had a muscle strain.
Greece’s Tsitsipas, 21, will face Canadian Milos Raonic or Cristian Garin of Chile in the third round.
Among the other men playing second-round matches on Wednesday are 20-time Grand Slam champion Roger Federer and Spanish ninth seed Roberto Bautista Agut.
You can listen to live commentary on some of the day’s action from 07:00 GMT on Tennis Breakfast on BBC 5 Live Sports Extra and follow live text commentary.