Nadal cruised past South Africa's Kevin Anderson 7-5, 6-1, 6-4, while Murray beat 10th-seeded Grigor Dimitrov of Bulgaria 6-4, 6-7 (5-7), 6-3, 7-5.
The 14-time Grand Slam champion Nadal beat Roger Federer in the 2009 Aussie final and is a two-time runner-up in Melbourne, including last year when he was stunned by Stan Wawrinka in the final. Nadal, of course, is the reigning French Open king.
Nadal will play in the quarterfinals here for the eighth time. He will next face seventh-seeded Czech Tomas Berdych, who defeated Bernard Tomic 6-2, 7-6 (7-3), 6-2.
Berdych is through to the quarterfinals in Melbourne for the fifth straight year.
Murray, a three-time Aussie Open runner-up, was almost taken to a fifth set on Sunday. The Brit saved a set point while serving at 5-2 down in the fourth set, then got it back on serve at 5-5, broke Dimitrov to love -- which prompted the 23-year-old to destroy his racquet -- and then served out.
The victory sends Murray to an Australian Open quarterfinal for the sixth straight year, and came against an opponent who ended his Wimbledon 2013 title defense in the quarterfinals last year.
Murray also reached his 16th straight Grand Slam quarterfinal. The last time Murray failed to reach the last eight at a major was when he lost in the third round at the 2010 U.S. Open to Wawrinka.
Next up for Murray is Australian Nick Krygios, who rallied past Andreas Seppi of Italy 5-7, 4-6, 6-3, 7-6 (7-5), 8-6. Seppi was trying to build off his monstrous upset of Federer in the third round.
Krygios, who saved a match point, became the first Australian man to reach the quarterfinals here since Lleyton Hewitt in 2005.