Swiss Grand Slam master Federer was stung into action after losing the first set to reel in Italian Simone Bolelli in four sets and take his place in the seeded round.
Murray, a three-time runner-up in Melbourne, extended his record against Australian opponents to 10-0 with a consummate straight sets victory over Marinko Matosevic.
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World number three Rafael Nadal was bidding to join them in his night match against American qualifier Tim Smyczek on Rod Laver Arena.
Second seed Federer, chasing his fifth Australian Open title, problem-solved his way to a 3-6, 6-3, 6-2, 6-2 win over Bolelli and will play another Italian Andreas Seppi in the third round.
The 17-time Swiss Grand Slam champion, who developed a mystery swollen finger during the contest, lost the opening set after the only break on his serve, but he found a solution and swept through the next three sets.
"It's always a good feeling fighting your way out of a match, winning the last three sets convincingly and actually playing really positive tennis," Federer said.
"Today I had to do some adjustments because he was doing things very well. By figuring things out it's a great feeling to have once you've got it."
Federer has always made the third round in 16 attempts in Melbourne and has reached the semi-final stage for the last 11 Australian Opens.
The Swiss legend was non-plussed by a swollen finger that may have been caused by a bee sting.
"It's the weirdest thing. I don't know. I feel it on the tip of my finger. I feel like it's numb and swollen," he said.
Murray got some payback on vocal local hope Matosevic as he cruised into the third round.
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