Federer, the record 17-time Grand Slam champion and chasing his fifth Australian title, made light work of his first outing of 2013 with a three-set demolition of Frenchman Benoit Paire on Tuesday.
Third seed Murray was equally impressive in clinically dismantling Dutchman Robin Haase, 6-3, 6-1, 6-3 to progress safely to the second round.
Elsewhere as temperatures climbed on the second day of the year-opening major, 2008 finalist Jo-Wilfried Tsonga won an all-French contest in straight sets over Michael Llodra, while big-serving Canadian 13th seed Milos Raonic took four sets to oust Jan Hajek.
Second seed Federer showed few signs of rustiness in his first match of the year as he demolished the 46th-ranked Paire 6-2, 6-4, 6-1 in 1hour 23 minutes at the Rod Laver Arena.
The 31-year-old Swiss maestro gave Paire little respite with six service breaks, while his own serve was rock-solid with no breaks conceded.
There was little Paire could do to stop the cascade of winners off the racquet of Federer, who is bidding to become only the second man after Australia's Roy Emerson to win five Australian Open titles.
"I'm very happy with the first round match, total control," Federer said.
"He can be a tricky opponent, but I guess his playing style doesn't disturb me that much overall.
"I'm happy I was able to play a clean match out there today."
Murray, 25, was authoritative in his first match in Melbourne, needing just 1 hour 37 minutes to take apart the erratic Haase with eight service breaks and making just 20 unforced errors in the 25 games.
Much has changed in Murray's life since his career-transforming victory over world number one Novak Djokovic in last year's US Open final, and he is among the favourites at the year's opening major tournament.