The Russian world number two ended Chinese hopes by swatting aside 21st seed Peng Shuai 6-3, 6-0 as she lifts her game the deeper she gets in the tournament.
It hands organisers a dream last eight clash between two of the most marketable players on tour with Canadian seventh seed Bouchard surviving a mid-match slump to defeat unseeded Irina-Camelia Begu of Romania in three sets.
Nadal, a 14-time Grand Slam champion, was dominant after a tight first set against power-hitting South African Kevin Anderson, running out a 7-5, 6-1, 6-4 winner and will next play Czech Tomas Berdych for a place in the semi-finals.
"After a tough period of time for me it's a fantastic result and I'm very happy with the way I played today," said Spain's Nadal, who came into the tournament after a three-month injury layoff.
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"It was probably my best match here this year so that's very important for me and very special."
Berdych admitted he would have to be at the top of his game to beat Nadal.
"I'm going to have to sit down with my team and prepare the right tactics," he said
Another Australian, Nick Kyrgios, will attempt to down Roger Federer's shock conquerer Andreas Seppi of Italy later Saturday while Britain's Andy Murray has a tough task against 10th seed Grigor Dimitrov.
Sharapova, gunning for a sixth Grand Slam title and her first in Australia since 2008, said her match against Peng was tougher than the score suggested.
"I've always had a little trouble against Peng Shuai, she's a really tough competitor," she said.