On a scorching day at Melbourne Park, the bad boy of tennis Down Under had two chances to secure victory at Rod Laver Arena on 120th-ranked Brands' serve at 6-5 in the fourth set.
Brands saved them both, and another five in the decisive tiebreak, before Tomic closed it out 10-8 to set up a likely third-round match with Roger Federer, who will play Russia's 40th-ranked Nikolay Davydenko in the evening session.
"I would prefer to play Davydenko," Tomic said in a courtside interview, raising a laugh in the stadium where players and spectators alike baked in 40 degree Celsius heat.
"I definitely got my arse kicked (by Federer) both times," added 43rd-ranked Tomic, who was beaten by the Swiss maestro in the fourth round of last year's tournament and later in the year at Cincinnati.
Tomic sealed victory shortly before his countryman James Duckworth succumbed in a marathon five-setter to Slovenian Blaz Kavcic.
Duckworth's loss left the much-vaunted Tomic the sole hope for local fans, who on Wednesday mourned ninth seed Sam Stosur's second round exit from the women's draw.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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