Andersons devastating performance helped England bowl South Africa out for just 119 and inspired a seven-wicket victory in the fourth one-day international.
South Africa, who had elected to bat, were shot out in 36.5 overs. England overtook their score within 32 overs, with Jonathan Trott celebrating an unbeaten half-century.
Stuart Broad removed Graeme Smith in the second over and Anderson then struck two blows, dismissing Hashim Amla and JP Duminy as the hosts slumped to 35 for three.
AB de Villiers, fresh off an imperious match-winning century in the third ODI, played some commanding strokes early on as he scored 22 before Tim Bresnan zipped a delivery into his pads and won an lbw decision, despite the ball being in danger of missing leg-stump due to his wide angle of delivery.
Anderson then returned for a superb spell of three for six in four overs that effectively settled the match.
South Africas total of 119 was their lowest in a home one-day international.
England openers Andrew Strauss and Trott then eased their way to 74 before off-spinner Johan Botha trapped the visiting captain leg-before for 32 and had Kevin Pietersen caught for three in a fine spell of two for 22 in eight overs.
Trott stayed through to the end, however, scoring a top-class 52 not out off 77 balls, while Eoin Morgan made 28 not out in 40 balls in the canter to victory.
South Africa will attempt to level the series in the final match in Durban on