Top-ranked Nadal was broken by Tommy Haas for the first time in the tournament, but showed no weakness in ripping 53 winners to only eight unforced errors in a 6-4, 6-2, 6-2 victory.
"I think I played one of my best matches here at the Australian Open," said Nadal, making his fifth appearance at Melbourne Park.
He will face 13th-seeded Fernando Gonzalez of Chile, who beat Nadal in straight sets en route to a runner-up finish in 2007, who needed more than 4 hours to beat France's Richard Gasquet with a 12-10 fifth set.
The fourth-seeded Murray, seeking his first Grand Slam title, ran off 11 straight games while overwhelming Jurgen Melzer 7-5, 6-0, 6-3. The 21-year-old Scot had only 10 unforced errors and next plays No. 14 Fernando Verdasco.
"I hope I can keep this form up," Murray said. "I'm going to have to play my best every match to have a chance."
Serena Williams wasn't her sharpest, but she hasn't had to be so far. And there were no distractions as she beat overmatched China's Peng Shuai 6-1, 6-4.
Williams, still chuckling about the man who dashed on court half-naked during her doubles match Friday, overcame two service breaks in the second set to keep alive her pursuit of a 10th Grand Slam title.
With Haas playing at the top of his game, Nadal fell behind 2-0 in the first set, then never faced another breakpoint. He lost only 13 points in 12 service games and committed only one unforced error in the 43-minute second set and two in the third.
The crowd favorite for Murray's match was clear, 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 held while down 3-0 in the third set to end Murray's streak of 11 games.
Melzer broke as Murray served for the match at 5-1 and fended off double match point in the next game. But Murray finished it off with his eighth ace, 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 - just six minutes longer than Gonzalez and Gasquet were on court Saturday - thanks in part to a 45-minute effort when Andrei Pavel retired in the first round with a bad back.
With fans screaming after every point like a Davis Cup match, Gonzalez saved a match point in the third-set tiebreaker, then a break point in the 21st game of the fifth set. The Beijing Olympics silver medalist broke Gasquet in the next, setting up match point with a perfect lob and clinching it with a backhand winner.
The mood seemed almost subdued as play got under way at Melbourne Park, a day after the streaker and a violent clash between Serbian and Bosnian fans kept security guards busy. A chair-flinging skirmish after defending champion Novak Djokovic of Serbia beat Bosnian-born American Amer Delic left a woman injured, three men charged with riotous behavior and 30 people ejected by police.
Williams became increasingly frustrated against Peng as she was broken twice early in the second before pulling herself together.
"I started making more errors and then I lost my serve a couple times," she said. "Then I think I put too much pressure on myself. Then, next thing I know, I was down."
Luckily for Williams, that's not necessarily a bad thing.
"I was like, 'You know, Serena, sometimes you just play better when you're down.' I started playing better."
Her concentration was severely challenged when the streaker danced his way on court a day earlier.
"I noticed he didn't have underwear on. I thought, 'OK, I must be seeing things.' Then I just thought, my eyes, my innocent eyes,'" she said, smiling.
Williams next faces No. 13 Victoria Azarenka of Belarus, who ousted 2006 Australian Open and Wimbledon champion Amelie Mauresmo.
Olympic gold medalist Elena Dementieva extended her winning streak to 13 matches, beating Australia's Samantha Stosur. Carla Suarez Navarro, who had an upset win over reigning Wimbledon champion Venus Williams in the second round, beat fellow Spaniard Maria Jose Martinez Sanchez.
Also advancing were No. 21 Anabel Medina Garrigues, who ousted 12th-seeded Flavia Pennetta of Italy, and No. 18 Dominika Cibulkova of Slovakia.
The Bondarenko sisters of Ukraine both were ousted, missing out on a fourth-round meeting. Kateryna lost to No. 22 Zheng Jie of China and older sister Alona fell to No. 8 Svetlana Kuznetsova, the 2004 U.S. Open champion.
No. 14 Fernando Verdasco of Spain beat No. 22 Radek Stepanek to advance along with three Frenchmen Saturday.
Among them was fifth-seeded Jo-Wilfried Tsonga, the runner-up here last year, who beat Israeli Dudi Sela and next meets No. 9 James Blake, who became the second American to reach the final 16, joining Andy Roddick.
Gael Monfils, a French Open semifinalist last year, beat No. 17 Nicolas Almagro of Spain and will face No. 6 Gilles Simon, who ousted No. 19 Mario Ancic of Croatia.