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Nadal
overpowered the 15th-ranked Anderson 7-5, 6-1, 6-4 in 2hr 6min on Rod
Laver Arena and will face Czech seventh seed Tomas Berdych in the last
eight.
It will be Nadal's eighth quarter-final appearance as he bids for his second Australian title after losing to Stan Wawrinka in last year's decider.
Nadal, who won the Open in 2009, showed no signs of the health problems he suffered when taken to five sets by American Tim Smyczek in the second round and looked back to his best.
"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.
"It was probably my best match here this year so that's very important for me and very special."
Anderson had no trouble and dropped only one point in his first five service games before he cracked serving for a tiebreaker.
Nadal got to 15-40 and held two set points, but the South African conceded the opening set when he made an ugly-looking crouch forehand into the net.
Nadal, who had been struggling to handle Anderson's serve, suddenly found himself a set up in 52 minutes.
The South African's confidence dipped and Nadal swiftly seized the initiative, breaking his opening two service games to take the second set in 32 minutes.
Nadal quickly grabbed an early break in the third set to strengthen his grip and take the match and now has a 18-3 record against Berdych.
