The top seed moved majestically as he made a statement on Centre Court, winning 6-1 6-4 6-2 in just two hours.
Djokovic breezed into a 3-0 lead in an opening set he served out to love after breaking for a second time, returning majestically as he dominated the Australian.
The 20-time grand slam champion needed just the one early break in the second set as he served superbly and was ruthless at the net, while also bossing rallies from the back of the court.
World number three Djokovic was relentless as he broke twice in a one-sided third set before ending the match with a hold after saving the only break point he faced.
Six-time Wimbledon champion Djokovic will face fellow Serbian Miomir Kecmanovic in round three at the All England Club.