Nadal came into the opening grand slam of the season short of match practice and survived an almighty scare when sick on court and taken to five sets by American Tim Smyczek in the second round.
But with each passing match, the world number three looks to be building momentum.
He took just over two hours to see off 15th-ranked Anderson 7-5 6-1 6-4 on the Rod Laver Arena.
The Spaniard oozed confidence after his victory as he bids for his second Australian Open title.
"After a tough period of time for me it's a fantastic result and I'm very happy with the way I played today," he said in his courtside interview.
"It was probably my best match here this year so that's very important for me and very special."
Nadal, beaten by Stanislas Wawrinka in a dramatic final in Melbourne last year, will face Czech seventh seed Tomas Berdych in the last eight.
Berdych will doubtless prove a dangerous opponent and showed his intentions with a straight sets victory over Australian hope Bernard Tomic in their last 16 clash Sunday, but he has a 3-18 career record against Nadal.
The route to the final in that half of the draw has been eased by the upset exit of second seed Roger Federer to Andreas Seppi of Italy Friday.
Seppi looked set to build on those heroics when he took a two-set lead against the poster boy of the championships, 19-year-old Nick Krygios, but the Australian teenager was made of sterner stuff.
He fought back to level -- saving a match point in the fourth set-- and amid a mounting frenzy on the Hisense Arena took the deciding set 8-6 after over three and a half hours of riveting action.
The 5-7 4-6 6-3 7-6 8-6 victory earned him a quarterfinal against two-time grand slam champion Andy Murray.
The British star's match with Bulgarian Grigor Dimitrov on the Rod Laver Arena was briefly interrupted by fans cheering Krygios' victory and there is a sure to be a partisan following for Tuesday's intriguing clash with a semifinal berth at stake.
Murray had to dig deep to avenge his Wimbledon defeat last year to Dimitrov, rallying from 2-5 down in the fourth set before closing out a 6-4 6-7 6-3 7-5 victory.
In the women's singles, Maria Sharapova and Eugenie Bouchard set up their eagerly-awaited quarterfinal clash with contrasting victories Sunday.
Second seed Sharapova was rarely troubled in dispatching 21st seed Peng Shuai of China, 6-3 6-0, while Canadian Bouchard struggled to defeat Irina-Camelia Begu of Romania 6-1 5-7 6-2.
Bouchard, who has had to cope with increased media attention after the "Twirlgate" controversy, lost concentration to drop the second set, but was impressive in the opener and the decider.
She has never beaten Sharapova, one of her inspirations but came close in the semifinals of last year's French Open.
Five-time grand slam winner Sharapova conceded as much when asked to reflect on the upcoming clash Tuesday.
"It was a really tough three setter. She's been playing incredibly well -- confident aggressive tennis. I have a tough match ahead of me," she said.
Third seed Simona Halep of Romania later joined them in the last eight, battling past Belgian Yanina Wickmayer 6-4 6-2 to earn a match with Russian 10th seed Ekaterina Makarova.