Nadal, the top seed, was nearly perfect, making only eight unforced errors in beating Tommy Haas 6-4, 6-2, 6-2. The 22-year-old Spaniard is bidding to win his first Australian Open and prevent second-seeded Roger Federer from tying Pete Sampras' all-time record of 14 Grand Slam singles titles.
Nadal had his serve broken in the second game of the match, the first time he dropped serve in the tournament.
After losing a semifinal last year to unheralded Jo-Wilfried Tsonga of France, Nadal is wary of being overconfident.
"Perfect matches doesn't exist," he said, a touch dismissively, when asked if his game was beyond improvement as he dismantled Haas, a semifinalist here two years ago. "Always you can improve, no?"
Fourth-seeded Murray, meanwhile, ran off 11 straight games in another dominating performance, overwhelming Jurgen Melzer 7-5, 6-0, 6-3. Murray, seeking his first Grand Slam title, had only 10 unforced errors, including just two in the second set, and overcame a brief lapse toward the end.
"I'm sure one match in a Slam, if you want to go deep, maybe you're not playing your best tennis, you have to try and find a way through to win," said Murray, predicting a tougher challenge as the tournament enters its second week. "I hope it doesn't happen, but if it does, I need to be prepared to try and win a match when I'm not playing my best tennis."
The 21-year-old Scot next faces No. 14 Fernando Verdasco. Nadal will play Chile's Fernando Gonzalez, who came back from two sets down to beat Richard Gasquet of France, 3-6, 3-6, 7-6 (10), 6-2, 12-10 in a four-hour marathon.
Gonzalez, a 2007 finalist at Melbourne Park, saved a match point in the third set tiebreak before he fought back to win the match, in which the fifth set alone lasted 88 minutes.
Gonzalez was on the court two hours before Nadal, but their matches both finished around midnight.
"My body is still alive," Gonzalez said. "I have 48 hours, maybe a little bit less. But I want to enjoy this moment. I think I won a really tough match that I will remember for the rest of my life."
Ninth-seeded American James Blake also reached the fourth round on Saturday.
Blake beat No. 18 Igor Andreev of Russia 6-3, 6-2, 3-6, 6-1 to set up a clash with fifth-seeded Tsonga, one of three Frenchmen to make it through to the fourth round.
The crowd in Hisense Arena was definitely pro-Murray, with Scottish flags and tartan hats scattered about on a cool night.
Constantly confounded by Murray's blend of power, speed and spin, Melzer did get a huge ovation when he rallied from 15-40 to hold while down 3-0 in the third set to end Murray's streak of 11 games. He had double break point as Murray served in the next game, only to see the him rally.
Melzer broke as Murray served for the match at 5-1 and fended off double match point in the next game. But Murray easily held in the next, finishing it off with his eighth ace and getting one step closer to becoming the first British man to win a major since 1936.
Sometimes sprinting to his chair during changeovers, Murray has raced through his first three matches in a combined 4 hours and 15 minutes, thanks in part to a 45-minute effort in the first round match when Andrei Pavel retired with a bad back.
It has been 81 years since Jean Borotra provided France with its only Australian Open men's singles champion, but there is a real hope of a breakthrough this year.
"It's time for us," Simon said. "If it's not now, it's never."
Simon said all of the Frenchmen, who have been friends since they were children, got a real confidence boost out of seeing Tsonga reach the Australian Open final in 2008.
"We know that we are all very good players but there is not one better than the others," Simon said. "To see him reach the final, it was really, really good for us and for our confidence.
"Finally, we just saw that we were able to do it. That's why I think we had a great year last year."
Simon made the third round at three of the four Grand Slams last year but had never made it the fourth round of the majors until this year in Melbourne.
The good news for France is it is guaranteed at least one quarterfinalist this year, but the bad news is it's certain to lose one player after Simon and Monfils play each other in the next round.
"At the moment we've just played against players we know we can defeat," Simon said. "It was hard but we just did our job. The next ones will be the tough ones.
"I think every day maybe we can all lose, on the same day, but for the moment, we are still here."
Information from The Associated Press and Reuters was used in this report.