The Swiss maestro needed only an hour and 39 minutes to claim a convincing 6-2 6-3 6-2 win over the 47th-ranked Romanian.
Not even a late appearance by Prince William, who is on a three-day tour of Australia, at the Rod Laver Arena could overshadow the record grand slam winner's victory charge as he marched into the third round.
Federer had been below his best in his opening match against Igor Andreev, when he dropped a set in the first round at a major for the first time in six years, but he immediately looked in the mood as he crashed 20 winners in an opening set that lasted 34 minutes.
The second set was captured in one minute fewer, despite Hanescu managing to grab three games, with the Swiss continuing to pepper the lines with winners.
Federer had already raced into a 3-0 lead in the third set when Prince William arrived, to the applause of the near-capacity 14,000 crowd, just an hour and 15 minutes after the start of the game.
The Prince's schedule has been hectic during his brief tour Down Under and Federer hardly took up much of his time as he quickly wrapped up the match when Hanescu blocked a return long.
"I knew the danger of Victor. He is a good player although maybe he is more accustomed to clay," Federer said afterwards.
"I am just thrilled to be through."