Anderson, seeded 19th for the tournament, will face unseeded Frenchman Edouard Roger-Vasselin on Friday.
Should the big-serving South African progress to the fourth round, he could meet his nemesis, the seventh-seeded Tomas Berdych.
Anderson scraped through the first round, beating Czech Republic’s 82nd-ranked Jiri Vesely 2-6, 6-7 (4/7), 6-4, 6-4, 6-4, in his opening match in Melbourne.
– Sapa
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