Edmund, the main British man in the singles draw, won 6-7 (4-7) 6 3 6-3 6-4 in the first round in Melbourne.
The 23-year-old, positioned 49th, twice returned from a set down and recouped from 2-0 behind in the last set to win in a moment shy of four hours.
He goes ahead to confront Uzbekistan's Denis Istomin in the second round.
Edmund's best past triumph at a Grand Slam competition, as far as rankings, had been his prevail upon fifteenth seed Richard Gasquet at the 2016 US Open.
He had lost his lone past experience with Anderson more than five sets finally year's French Open, and was in no disposition to endure a comparable thrashing by the South African.