Reigning US Open champion Murray downed Dutchman Robin Haase 6-3 6-1 6-3, while Federer was untroubled in ousting Frenchman Benoit Paire 6-2 6-4 6-1.
Murray broke one of world sport's most famous ducks when he won his first grand slam final in five attempts at Flushing Meadows last year, beating world No.1 Novak Djokovic in the decider.
The third seed carried that form into the first major of 2013, belting Haase in just one hour and 37 minutes.
"It (being a grand slam winner) didn't feel much different to me," said the 25-year-old Murray, who became Britain's first male major winner in 76 years.
"I was still nervous before I went on to play the match.
"I think when I would see the benefits of that is if I get myself deep into a slam this year and you're playing against the top players - that's when you'll draw on that experience and use it in the right way.
"But I don't think it makes a huge amount of difference to how you feel at the beginning of events.
"... I'm focused on this event and I trained really hard to get myself ready for it.
"So whether everyone else is thinking about the US Open or not makes no difference to me."
Murray, the runner-up at Melbourne Park in 2010 and 2011, will play Joao Sousa form Portugal in the second round.
Sousa also advanced with a minimum of fuss, beating Australian wildcard entrant John-Patrick Smith 6-4 6-1 6-4.
Federer extended his record haul of major titles to 17 at Wimbledon last year when he downed Murray in the final.
The pair are seeded to meet in the semis at Melbourne Park.
Federer was happy with his effort against Paire in his first competitive match since last year's world tour finals in London.
"I've had a few busy years since having kids and I wanted to cool it down a bit," said the Swiss superstar.
"It's nice to enjoy the off-season and have another two weeks off.
"I'm confident in my play and I'm looking forward to my next match."
Federer will play either Russian Nikolay Davydenko or Israel's Dudi Sela in the second round.
Jo-Wilfried Tsonga, the 2008 Australian Open runner-up, won his all-French clash with Michael Llodra 6-4 7-5 6-2.
No.13 seed Milos Raonic from Canada started slowly in his first-round clash with Czech Jan Hajek before lifting to win 3-6 6-1 6-2 7-6 (7-0).