With Victoria Azarenka a class apart in her third-round win, Nadal stormed past France's Gael Monfils 6-1, 6-2, 6-3 to underline his challenge to Novak Djokovic's three-year Melbourne reign.
Federer was typically fluent in his 6-2, 6-2, 6-3 win against Teymuraz Gabashvili and Murray, continuing his strong recovery from back surgery, was a convincing winner over Feliciano Lopez.
With sharply cooling temperatures bringing an abrupt end to four days of 40 Celsius (104 Fahrenheit), there was a businesslike feel as the men's and women's contenders set about reaching week two.
"It was a tough year last year and it took some time to figure out what I needed to do to feel better and to get my confidence back, because that's what I thought it was mostly," said Federer, seeded six.
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"For the last four to five months I feel that I'm back to normal again and at least I feel I've done the work to catch up and haven't had any setbacks, so it's very positive."
"Today was a big step up for me. Feliciano is a top-30 player. He's a tricky opponent to play," Murray said.
In the evening session, Nadal was superior in all departments to the entertaining but inconsistent Monfils, winning in just over two hours.
Nadal will next face Japanese number one Kei Nishikori, who reeled off the last 10 games against Donald Young to end American interest in the men's competition.