Federer beat Serbian Filip Krajinovic in straight sets to set up a third round match against local lad John Millman.
Chances of the Swiss world no.3 setting up a date with Serbian world no.2 Novak Djokovic also remained alive after the latter beat Japanese wild card Tatsuma Ito in straight sets. Ito had beaten India's Prajnesh Gunneswaran in his first round outing to set up the match against the defending champion.
Greek world no.6 Stefanos Tsitsipas had a walkthrough after his opponent Philipp Kohlschreiber of Germany withdrew from the match.
In the women's singles Serena beat Slovenia's Tamara Zidansek in straight sets to go through to the next round. She will now face China's Qiang Wang. Japanese third seed Naomi Osaka meanwhile will face US teen sensation Coco Gauff after beating China's Saisai Zheng in straight sets. 15-year-old Gauff had made it to the second round after beating compatriot and tennis great Venus Williams in three sets. She prevailed over Romania's Sorana Cirstea to set up the clash against Osaka.
Top seed and local favourite Ahsleigh Barty will face Kazakhstan's Elena Rybakina in the third round after prevailing over Slovenian Polona Hercog.
Denmark's Caroline Wozniacki, who will be retiring from professional tennis after the Australian Open, faces Tunisian Ons Jabeur in the third round after beating Ukrainian Dayana Yastremska in straight sets. Czech world No. 8 Petra Kvitova faces Russia's Ekaterina Alexandrova in the third round.
( With inputs from IANS )