The 33-year-old was in virtuoso form to charge past the 27th seed 6-1, 6-2, 6-4 in hot sunshine on Rod Laver Arena and make the round of 16 at Melbourne Park for a 13th time.
The world number three defeated Millman in the third-round 4-6, 7-6, 6-4, 4-6, 7-6 in about four hours and five minutes.
Roger Federer almost always plays on the centre court where he has won six titles, and Millman is keen to disrupt his momentum.
Rafael Nadal can only count one Melbourne title among his 19 Majors but he will be confident of reaching the third round.
The six-time champion first played at Melbourne Park in 2000 and has gone on to make the semi-finals or better on 14 occasions, with no exits before round three.
Jannik Sinner, a former champion skier before switching to tennis, swept past Max Purcell 7-6 (7/2), 6-2, 6-4 at the Australian Open.
Roger Federer will play either French qualifier Quentin Halys or Serbian Filip Krajinovic in the second round of Australian Open.
The 36-year-old Belgian, who retired after the 2012 US Open, is set for a return in March, having originally scheduled her comeback at next week's Australian Open until a knee injury happened.
Nadal, currently No. 1 in the ATP rankings, and Djokovic, who is No. 2 ahead of Federer, each took home two major trophies last season.
Brayden Schnur won his first round contest over Sebastian Ofner in a match which took place in smoky conditions.
Players who took part included Rafael Nadal, Roger Federer, Serena Williams, Caroline Wozniacki and Alexander Zverev.
Check out the five players to watch in the men's draw at the Australian Open, the first Grand Slam tournament of the season.
Novak Djokovic is gunning for his eighth crown and Federer his seventh, having last lifted the Australian Open in 2018.
Tsitsipas gets his tournament underway against rising Canadian star Dennis Shapovalov on Friday morning.
The match, originally slated for Bogota's Movistar arena on November 22, was called off minutes before its scheduled start amid fears of violence.