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 goes 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.
But Sharapova's boyfriend Grigor Dimitrov was turfed out by never-say-die British sixth seed Andy Murray, who won the last five games to battle through a pulsating night match on Rod Laver Arena 6-4, 6-7 (5/7), 6-3, 7-5.
The consistent Berdych, who made the final four last year, ended Australian Bernard Tomic's tournament with a comfortable 6-2, 7-6 (7/3), 6-2 hit-out.
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"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.
"It was probably my best match here this year so that's very important for me and very special."
"Whatever I need to do I'm going to be ready for it and will try to fight until the last point," he said.
Another Australian, teenager Nick Kyrgios, managed to achieve what Roger Federer could not by beating dogged Italian Andreas Seppi 5-7, 4-6, 6-3, 7-6 (7/5) 8-6.
The 19-year-old becomes the first home-grown quarter-finalist in Melbourne since Lleyton Hewitt in 2005 with a face-off against Murray his reward.