The 20-year-old will face either Marcos Baghdatis or second seed Rafael Nadal in the third round.
Cypriot Marcos Baghdatis eased past Frenchman Richard Gasquet, the fourth seed, with a 6-4 6-4 win.
The 23-year-old Scot, still yet to drop a set at the event, next plays Jurgen Melzer who beat Marcos Baghdatis.
The Croatian world No. 11 will next play fifth seed Marcos Baghdatis of Cyprus, who beat 2007 champion Philipp Kohlschreiber 6-3 6-4.
Murray will meet Marcos Baghdatis in the third round after his Cypriot opponent Grigor Dimitrov retired through injury when trailing 7-5 4-1.
Second seed Marcos Baghdatis suffered a 6-3 6-4 defeat by Robin Haase.
The fourth seed beat American Tim Smyczek 6-0 7-5 4-6 6-3 and will now play 2006 Australian Open runner-up Marcos Baghdatis .
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France's Jo-Wilfried Tsonga will meet Tomas Berdych, from the Czech Republic, in the last eight after he beat Marcos Baghdatis 6-2 7-6.
The Argentine won 6-3, 6-4, and will now face unseeded Bulgarian Grigor Dimitrov who came from a set down to beat Marcos Baghdatis.
Argentine Nalbandian, a former SW19 finalist, lost in straight sets to Marcos Baghdatis while Safin went down meekly to eventual champion Roger Federer.
As the fourth seed he receives a bye through to the second round, at which point he will meet Marcos Baghdatis or Sam Querrey.
In other first round matches, Ukraine's Alexandr Dolgopolov beat Marcos Baghdatis of Cyprus 6-4 6-4 and Spain's Nicolas Almagro defeated Poland's Lukasz Kubot 7-5 6-2.
Meanwhile second seed Marcos Baghdatis has been forced to pull out of the tournament because of a shoulder injury he suffered in practice on Sunday.
Also advancing were No. 22 Fernando Verdasco, No. 28 Marcos Baghdatis, the 2006 Australian Open runner-up, No. 31 Radek Stepanek and No. 32 Julien Benneteau.
The World No.3 will play Grigor Dimitrov of Bulgaria who reached his first ATP final by edging out Marcos Baghdatis of Cyprus 6-3 5-7 7-6.
He was joined by the Czech Republic's Tomas Berdych after the second seed's opponent, Marcos Baghdatis, retired hurt with a foot injury in the first set.
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The other semifinal will be between 2006 Australian Open finalist Marcos Baghdatis of Cyprus and 21-year-old Bulgarian Grigor Dimitrov, who upset Austrian seventh seed Jurgen Melzer.
But the 2002 champion clawed the break back and then struck again for a 6-4 6-4 4-6 7-5 win and a last eight match with Marcos Baghdatis.
Simon, who reached the semifinals in Brisbane last year, will play Marcos Baghdatis in the next round after the Cypriot defeated sixth-seeded German Florian Mayer 6-4 6-2.
Haas will be playing his first quarterfinal of the year against Cypriot Marcos Baghdatis, who beat qualifier Dustin Brown 1-6 6-4 6-1 in one hour and 47 minutes.
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Elsewhere, the No. 4 seed Juan Martin del Potro was forced to save three match points during a hard fought 4-6 6-4 7-6 victory over Cypriot Marcos Baghdatis .
On Tuesday, Cypriot tennis star Marcos Baghdatis threw a spectacular on-court tantrum at the Australian open, deliberately smashing four rackets in a row during a break between sets.
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Seventh seed Marin Cilic edged out Marcos Baghdatis 6-3 6-4 while Mardy Fish -- who knocked out holder Andy Murray -- continued his fine form with a 7-5 6-3 win over Feliciano Lopez.
Djokovic's fourth round clash against Marcos Baghdatis on Sunday night ran into the early hours of Monday, but the third seed's request to play Roddick in a night match fell on deaf ears.
Djokovic finished off Querrey at about 10 minutes shy of 2 a.m. and although it's nothing compared with the Australian Open day(s) in 2008 when Lleyton Hewitt beat Marcos Baghdatis at 4:34 a.m.
In other first-round matches, 2006 Australian Open finalist Marcos Baghdatis of Cyprus beat American Mardy Fish 7-5 7-5 to earn a second round clash against fourth-seed Tomas Berdych, who beat Australian qualifier Nick Lindahl in straight sets.
Spanish 10th seed Nicolas Almagro came from 2-1 down to beat Bulgaria's Grigor Dimitrov in five sets to book a tie with Swiss 21st seed Stanislas Wawrinka , who beat 2006 finalist Marcos Baghdatis of Cyprus, 7-6 6-4 5-7 6-1.
Other seeds such as Tommy Haas, Fernando Verdasco, David Ferrer, Lleyton Hewitt, Gael Monfils and Marin Cilic also progressed along with former tournament runners-up Jo-Wilfried Tsonga, Marcos Baghdatis and Rainer Schuettler, but former world No. 7 Richard Gasquet was eliminated.
Top seed Roger Federer of Switzerland went out to Marcos Baghdatis in the third round while Serbian ace Djokovic of Serbia joined him on the sidelines with a 7-5 6-3 defeat to Ivan Ljubicic of Croatia in their last 16 match.
It was a convincing performance at the end of a day on which just one seed fell out of the men's draw -- with 2006 finalist Marcos Baghdatis coming from two sets down to beat 17th seed David Ferrer 4-6 3-6 7-6 6-3 6-1.
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