The second seed beat the Australian in straight sets, winning 6-4 7-6 6-1.
Speaking on court after the match, the Swiss player said: "I kept on trying the whole second set. I thought the tie-breaker was going to go his way.
"I think overall we both played a great match, he's had a great run now and got the best out of me tonight.
"It's nice that you guys invite me back every year. It's not my favourite part of the job, beating up on the home heroes."
Federer will face Canadian Milos Raonic in the fourth round.