The 32-year-old debutant at the ATP's blue riband event won the first 11 games of the round-robin clash before a relieved Nishikori finally got on the scoreboard with an angled winner.
Normal service was quickly resumed though as Anderson closed out victory thanks to a 24th unforced error by Nishikori.
Only six-times champion Roger Federer has enjoyed a 6-0 6-0 victory at the season-ending tournament, that coming in 2005 in Shanghai against unfortunate Argentine Gaston Gaudio.
Anderson, the first South African to qualify for the eight-man event since 1995, made it two wins from two round-robin matches with a stunning display.
What made it all the more impressive was that Nishikori had beaten Federer in straight sets on Sunday and that Anderson had trailed the Japanese 3-5 in their head-to-head record.
Anderson, who opened with a straight sets win against Dominic Thiem, tops the Lleyton Hewitt group and will reach the semi-finals if Thiem beats Federer later. (Reporting by Martyn Herman; Editing by Hugh Lawson)
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