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It was a hard-fought victory for the 24-year-old South African, the match lasting just under two hours.
The lanky Anderson, ranked 61 in the world, made good use of his strong first serve, sending down 12 aces against his 64th-ranked opponent.
World No 8 Andy Roddick plays Cypriot Marcos Baghdatis in the evening session to determine Anderson's semifinal opponent.
Top seed Robin Soderling made it through to the quarterfinals with a 6-3 7-6 win over German journeyman Michael Berrer.
The world No 5 Swede broke the 58th-ranked Berrer once to claim the first set but was unable to penetrate the lanky 30-year-old's serve in the second.
Soderling prevailed in a tense 9-7 tiebreak to seal the hard-fought match in 95 minutes and set up a quarterfinal encounter with Australian qualifier Matt Ebden, who earlier upset eighth-seeded Uzbek Denis Istomin 6-4 6-4.
The double French Open finalist said he would be wary of the 196th-ranked Ebden as a player with nothing to lose as he warms up for the January 17-30 Australian Open.
"A couple of years ago when I played top ranked players I played without any pressure at all – and I always enjoyed the matches," he said.
"To me it was easier to play when I felt I had nothing to lose... There is always the possibility that I can lose if I am not 100 percent."
