Having reached the last 16 stage on no fewer than seven occasions in prestige grand slam tournaments, Anderson will, no doubt, be motivated to end what has become something of a bogey by finally qualifying for a grand slam quarter-final.
But a daunting prospect faces the 29-year-old big-server, who equalled his 14th-best world ranking this week, in that if he and third-seed and world No 3 Andy Murray both make it into the fourth round of the tournament they will meet in the last 16 round.
No South African has ever won a singles title at th US Open and no South African has made it into the quarter-final stage since Wayne Ferreira achieved the feat in 1992.
The best performances by any South Africans in reaching the final were achieved by Eric Sturgess in 1948 and Cliff Drysdale in 1965, with Sturgess losing a memorable finale of contrasting players to serve-and-volley legend Pancho Gonzalez after an epic 14-12 third set and Drysdale edged out by engaging Spanish stroke-making artist Manolo Santana.
The next best result by a South African in the US Open was achieved by Johan Kriek, who reached the semi-finals in both 1978 and 1979.
As for Anderson, the quest for a quarter-final berth begins in the first round against 17-year-old Russian prodigy, Andrey Rublev, with potential immediate opponents if he progresses including Colombian Santiago Giraldo, German Benjamin Becker, Uzbekistan's Dennis Istomin and Austrian Dominic Thiem.
But if Anderson is to reach the fourth round for the first time in the United States and go on to a memorable quarter-final for the first time in any grand slam tournament, the spectre of the formidable Murray will surely always be lingering in the background.
As for past head-to-head matches between the two, Murray has a 5-1 advantage, with victories in the last four meetings emphasising his advantage.